diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index bda5f8f4326f1..dc90bcf2239ac 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -328,6 +328,32 @@ class DatetimeLikeArrayMixin(ExtensionOpsMixin, AttributesMixin, ExtensionArray)
         _generate_range
     """
 
+    @property
+    def ndim(self):
+        return self._data.ndim
+
+    @property
+    def shape(self):
+        return self._data.shape
+
+    def __len__(self):
+        return len(self._data)
+
+    @property
+    def T(self):
+        # Note: we drop any freq
+        return type(self)(self._data.T, dtype=self.dtype)
+
+    def reshape(self, *args, **kwargs):
+        # Note: we drop any freq
+        data = self._data.reshape(*args, **kwargs)
+        return type(self)(data, dtype=self.dtype)
+
+    def ravel(self, *args, **kwargs):
+        # Note: we drop any freq
+        data = self._data.ravel(*args, **kwargs)
+        return type(self)(data, dtype=self.dtype)
+
     @property
     def _box_func(self):
         """
@@ -396,9 +422,6 @@ def size(self) -> int:
         """The number of elements in this array."""
         return np.prod(self.shape)
 
-    def __len__(self):
-        return len(self._data)
-
     def __getitem__(self, key):
         """
         This getitem defers to the underlying array, which by-definition can
@@ -1032,7 +1055,7 @@ def _add_nat(self):
 
         # GH#19124 pd.NaT is treated like a timedelta for both timedelta
         # and datetime dtypes
-        result = np.zeros(len(self), dtype=np.int64)
+        result = np.zeros(self.shape, dtype=np.int64)
         result.fill(iNaT)
         return type(self)(result, dtype=self.dtype, freq=None)
 
@@ -1046,7 +1069,7 @@ def _sub_nat(self):
         # For datetime64 dtypes by convention we treat NaT as a datetime, so
         # this subtraction returns a timedelta64 dtype.
         # For period dtype, timedelta64 is a close-enough return dtype.
-        result = np.zeros(len(self), dtype=np.int64)
+        result = np.zeros(self.shape, dtype=np.int64)
         result.fill(iNaT)
         return result.view("timedelta64[ns]")
 
diff --git a/pandas/core/arrays/datetimes.py b/pandas/core/arrays/datetimes.py
index 0335058a69c63..c0283915f7d92 100644
--- a/pandas/core/arrays/datetimes.py
+++ b/pandas/core/arrays/datetimes.py
@@ -76,6 +76,17 @@
 """
 
 
+def compat_2d(meth):
+    def new_meth(self, *args, **kwargs):
+        if self.ndim > 1:
+            result = meth(self.ravel(), *args, **kwargs)
+            return result.reshape(self.shape)
+        return meth(self, *args, **kwargs)
+
+    new_meth.__name__ = meth.__name__
+    return new_meth
+
+
 def tz_to_dtype(tz):
     """
     Return a datetime64[ns] dtype appropriate for the given timezone.
@@ -361,7 +372,7 @@ def __init__(self, values, dtype=_NS_DTYPE, freq=None, copy=False):
                 "ndarray, or Series or Index containing one of those."
             )
             raise ValueError(msg.format(type(values).__name__))
-        if values.ndim != 1:
+        if values.ndim not in [1, 2]:
             raise ValueError("Only 1-dimensional input arrays are supported.")
 
         if values.dtype == "i8":
@@ -818,6 +829,7 @@ def _sub_datetime_arraylike(self, other):
             new_values[arr_mask] = iNaT
         return new_values.view("timedelta64[ns]")
 
+    @compat_2d
     def _add_offset(self, offset):
         assert not isinstance(offset, Tick)
         try:
@@ -825,6 +837,7 @@ def _add_offset(self, offset):
                 values = self.tz_localize(None)
             else:
                 values = self
+
             result = offset.apply_index(values)
             if self.tz is not None:
                 result = result.tz_localize(self.tz)
diff --git a/pandas/core/arrays/timedeltas.py b/pandas/core/arrays/timedeltas.py
index 6c9462ff4fa4d..81588b0dee96d 100644
--- a/pandas/core/arrays/timedeltas.py
+++ b/pandas/core/arrays/timedeltas.py
@@ -222,7 +222,7 @@ def __init__(self, values, dtype=_TD_DTYPE, freq=None, copy=False):
                 "ndarray, or Series or Index containing one of those."
             )
             raise ValueError(msg.format(type(values).__name__))
-        if values.ndim != 1:
+        if values.ndim not in [1, 2]:
             raise ValueError("Only 1-dimensional input arrays are supported.")
 
         if values.dtype == "i8":
@@ -1076,7 +1076,7 @@ def sequence_to_td64ns(data, copy=False, unit="ns", errors="raise"):
         )
 
     data = np.array(data, copy=copy)
-    if data.ndim != 1:
+    if data.ndim not in [1, 2]:
         raise ValueError("Only 1-dimensional input arrays are supported.")
 
     assert data.dtype == "m8[ns]", data
diff --git a/pandas/core/ops/__init__.py b/pandas/core/ops/__init__.py
index 398fa9b0c1fc0..0e90a395d7f7e 100644
--- a/pandas/core/ops/__init__.py
+++ b/pandas/core/ops/__init__.py
@@ -12,7 +12,11 @@
 from pandas._libs import Timedelta, Timestamp, lib
 from pandas.util._decorators import Appender
 
-from pandas.core.dtypes.common import is_list_like, is_timedelta64_dtype
+from pandas.core.dtypes.common import (
+    is_extension_array_dtype,
+    is_list_like,
+    is_timedelta64_dtype,
+)
 from pandas.core.dtypes.generic import (
     ABCDataFrame,
     ABCExtensionArray,
@@ -24,6 +28,7 @@
 from pandas.core.construction import extract_array
 from pandas.core.ops.array_ops import (
     arithmetic_op,
+    array_op,
     comparison_op,
     define_na_arithmetic_op,
     logical_op,
@@ -350,7 +355,7 @@ def fill_binop(left, right, fill_value):
 # Dispatch logic
 
 
-def dispatch_to_series(left, right, func, str_rep=None, axis=None):
+def dispatch_to_series(left, right, func, str_rep=None, axis=None, eval_kwargs=None):
     """
     Evaluate the frame operation func(left, right) by evaluating
     column-by-column, dispatching to the Series implementation.
@@ -369,11 +374,57 @@ def dispatch_to_series(left, right, func, str_rep=None, axis=None):
     """
     # Note: we use iloc to access columns for compat with cases
     #       with non-unique columns.
+    eval_kwargs = eval_kwargs or {}
+
     import pandas.core.computation.expressions as expressions
 
     right = lib.item_from_zerodim(right)
+
     if lib.is_scalar(right) or np.ndim(right) == 0:
 
+        new_blocks = []
+        mgr = left._data
+        for blk in mgr.blocks:
+            # Reshape for EA Block
+            blk_vals = blk.values
+            if hasattr(blk_vals, "reshape"):
+                # ndarray, DTA/TDA/PA
+                blk_vals = blk_vals.reshape(blk.shape)
+                blk_vals = blk_vals.T
+
+            new_vals = array_op(blk_vals, right, func, str_rep, eval_kwargs)
+
+            # Reshape for EA Block
+            if is_extension_array_dtype(new_vals.dtype):
+                from pandas.core.internals.blocks import make_block
+
+                if hasattr(new_vals, "reshape"):
+                    # ndarray, DTA/TDA/PA
+                    new_vals = new_vals.reshape(blk.shape[::-1])
+                    assert new_vals.shape[-1] == len(blk.mgr_locs)
+                    for i in range(new_vals.shape[-1]):
+                        nb = make_block(new_vals[..., i], placement=[blk.mgr_locs[i]])
+                        new_blocks.append(nb)
+                else:
+                    # Categorical, IntegerArray
+                    assert len(blk.mgr_locs) == 1
+                    assert new_vals.shape == (blk.shape[-1],)
+                    nb = make_block(new_vals, placement=blk.mgr_locs, ndim=2)
+                    new_blocks.append(nb)
+            elif blk.values.ndim == 1:
+                # need to bump up to 2D
+                new_vals = new_vals.reshape(-1, 1)
+                assert new_vals.T.shape == blk.shape
+                nb = blk.make_block(new_vals.T)
+                new_blocks.append(nb)
+            else:
+                assert new_vals.T.shape == blk.shape
+                nb = blk.make_block(new_vals.T)
+                new_blocks.append(nb)
+
+        bm = type(mgr)(new_blocks, mgr.axes)
+        return type(left)(bm)
+
         def column_op(a, b):
             return {i: func(a.iloc[:, i], b) for i in range(len(a.columns))}
 
@@ -526,7 +577,7 @@ def wrapper(self, other):
         lvalues = extract_array(self, extract_numpy=True)
         rvalues = extract_array(other, extract_numpy=True)
 
-        res_values = comparison_op(lvalues, rvalues, op)
+        res_values = comparison_op(lvalues, rvalues, op, None, {})
 
         return _construct_result(self, res_values, index=self.index, name=res_name)
 
@@ -552,7 +603,7 @@ def wrapper(self, other):
         lvalues = extract_array(self, extract_numpy=True)
         rvalues = extract_array(other, extract_numpy=True)
 
-        res_values = logical_op(lvalues, rvalues, op)
+        res_values = logical_op(lvalues, rvalues, op, None, {})
         return _construct_result(self, res_values, index=self.index, name=res_name)
 
     wrapper.__name__ = op_name
@@ -723,7 +774,9 @@ def f(self, other, axis=default_axis, level=None, fill_value=None):
             if fill_value is not None:
                 self = self.fillna(fill_value)
 
-            new_data = dispatch_to_series(self, other, op)
+            new_data = dispatch_to_series(
+                self, other, op, str_rep=str_rep, eval_kwargs=eval_kwargs
+            )
             return self._construct_result(new_data)
 
     f.__name__ = op_name
@@ -749,7 +802,9 @@ def f(self, other, axis=default_axis, level=None):
             # Another DataFrame
             if not self._indexed_same(other):
                 self, other = self.align(other, "outer", level=level, copy=False)
-            new_data = dispatch_to_series(self, other, op, str_rep)
+            new_data = dispatch_to_series(
+                self, other, op, str_rep=str_rep, eval_kwargs={}
+            )
             return self._construct_result(new_data)
 
         elif isinstance(other, ABCSeries):
@@ -781,7 +836,9 @@ def f(self, other):
                 raise ValueError(
                     "Can only compare identically-labeled DataFrame objects"
                 )
-            new_data = dispatch_to_series(self, other, op, str_rep)
+            new_data = dispatch_to_series(
+                self, other, op, str_rep=str_rep, eval_kwargs={}
+            )
             return self._construct_result(new_data)
 
         elif isinstance(other, ABCSeries):
diff --git a/pandas/core/ops/array_ops.py b/pandas/core/ops/array_ops.py
index a225eec93b27e..c4cb2178c5035 100644
--- a/pandas/core/ops/array_ops.py
+++ b/pandas/core/ops/array_ops.py
@@ -56,7 +56,7 @@ def comp_method_OBJECT_ARRAY(op, x, y):
 
         result = libops.vec_compare(x, y, op)
     else:
-        result = libops.scalar_compare(x, y, op)
+        result = libops.scalar_compare(x.ravel(), y, op).reshape(x.shape)
     return result
 
 
@@ -156,12 +156,22 @@ def na_arithmetic_op(left, right, op, str_rep: str, eval_kwargs):
     return missing.dispatch_fill_zeros(op, left, right, result)
 
 
+def array_op(left, right, op, str_rep, eval_kwargs):
+    op_name = op.__name__.strip("_")
+    if op_name in {"eq", "ne", "lt", "le", "gt", "ge"}:
+        return comparison_op(left, right, op, str_rep, eval_kwargs)
+    elif op_name in {"and", "or", "xor", "rand", "ror", "rxor"}:
+        return logical_op(left, right, op, str_rep, eval_kwargs)
+    else:
+        return arithmetic_op(left, right, op, str_rep, eval_kwargs)
+
+
 def arithmetic_op(
     left: Union[np.ndarray, ABCExtensionArray],
     right: Any,
     op,
     str_rep: str,
-    eval_kwargs: Dict[str, str],
+    eval_kwargs: Dict[str, bool],
 ):
     """
     Evaluate an arithmetic operation `+`, `-`, `*`, `/`, `//`, `%`, `**`, ...
@@ -218,7 +228,7 @@ def arithmetic_op(
 
 
 def comparison_op(
-    left: Union[np.ndarray, ABCExtensionArray], right: Any, op
+    left: Union[np.ndarray, ABCExtensionArray], right: Any, op, str_rep, eval_kwargs
 ) -> Union[np.ndarray, ABCExtensionArray]:
     """
     Evaluate a comparison operation `=`, `!=`, `>=`, `>`, `<=`, or `<`.
@@ -256,10 +266,11 @@ def comparison_op(
 
     elif is_scalar(rvalues) and isna(rvalues):
         # numpy does not like comparisons vs None
+        # TODO: Should we be using invalid_comparison here?
         if op is operator.ne:
-            res_values = np.ones(len(lvalues), dtype=bool)
+            res_values = np.ones(lvalues.shape, dtype=bool)
         else:
-            res_values = np.zeros(len(lvalues), dtype=bool)
+            res_values = np.zeros(lvalues.shape, dtype=bool)
 
     elif is_object_dtype(lvalues.dtype):
         res_values = comp_method_OBJECT_ARRAY(op, lvalues, rvalues)
@@ -323,7 +334,7 @@ def na_logical_op(x: np.ndarray, y, op):
 
 
 def logical_op(
-    left: Union[np.ndarray, ABCExtensionArray], right: Any, op
+    left: Union[np.ndarray, ABCExtensionArray], right: Any, op, str_rep, eval_kwargs
 ) -> Union[np.ndarray, ABCExtensionArray]:
     """
     Evaluate a logical operation `|`, `&`, or `^`.
diff --git a/pandas/tests/arithmetic/test_period.py b/pandas/tests/arithmetic/test_period.py
index ed693d873efb8..d4fdeffa2c2db 100644
--- a/pandas/tests/arithmetic/test_period.py
+++ b/pandas/tests/arithmetic/test_period.py
@@ -755,18 +755,18 @@ def test_pi_sub_isub_offset(self):
         rng -= pd.offsets.MonthEnd(5)
         tm.assert_index_equal(rng, expected)
 
-    def test_pi_add_offset_n_gt1(self, box_transpose_fail):
+    def test_pi_add_offset_n_gt1(self, box_with_array):
         # GH#23215
         # add offset to PeriodIndex with freq.n > 1
-        box, transpose = box_transpose_fail
+        box = box_with_array
 
         per = pd.Period("2016-01", freq="2M")
         pi = pd.PeriodIndex([per])
 
         expected = pd.PeriodIndex(["2016-03"], freq="2M")
 
-        pi = tm.box_expected(pi, box, transpose=transpose)
-        expected = tm.box_expected(expected, box, transpose=transpose)
+        pi = tm.box_expected(pi, box)
+        expected = tm.box_expected(expected, box)
 
         result = pi + per.freq
         tm.assert_equal(result, expected)
diff --git a/pandas/tests/arrays/test_datetimes.py b/pandas/tests/arrays/test_datetimes.py
index c3cda22497ecb..acb419c09210f 100644
--- a/pandas/tests/arrays/test_datetimes.py
+++ b/pandas/tests/arrays/test_datetimes.py
@@ -23,9 +23,8 @@ def test_from_sequence_invalid_type(self):
     def test_only_1dim_accepted(self):
         arr = np.array([0, 1, 2, 3], dtype="M8[h]").astype("M8[ns]")
 
-        with pytest.raises(ValueError, match="Only 1-dimensional"):
-            # 2-dim
-            DatetimeArray(arr.reshape(2, 2))
+        # 2-dim allowed for ops compat
+        DatetimeArray(arr.reshape(2, 2))
 
         with pytest.raises(ValueError, match="Only 1-dimensional"):
             # 0-dim
diff --git a/pandas/tests/arrays/test_timedeltas.py b/pandas/tests/arrays/test_timedeltas.py
index 42e7bee97e671..ddfd2339e6c49 100644
--- a/pandas/tests/arrays/test_timedeltas.py
+++ b/pandas/tests/arrays/test_timedeltas.py
@@ -11,9 +11,8 @@ def test_only_1dim_accepted(self):
         # GH#25282
         arr = np.array([0, 1, 2, 3], dtype="m8[h]").astype("m8[ns]")
 
-        with pytest.raises(ValueError, match="Only 1-dimensional"):
-            # 2-dim
-            TimedeltaArray(arr.reshape(2, 2))
+        # 2-dim allowed for ops compat
+        TimedeltaArray(arr.reshape(2, 2))
 
         with pytest.raises(ValueError, match="Only 1-dimensional"):
             # 0-dim
diff --git a/pandas/tests/frame/test_query_eval.py b/pandas/tests/frame/test_query_eval.py
index 82c197ac054f0..f5f6c9ad6b3da 100644
--- a/pandas/tests/frame/test_query_eval.py
+++ b/pandas/tests/frame/test_query_eval.py
@@ -122,7 +122,8 @@ def test_ops(self):
                     result = getattr(df, rop)(m)
                     assert_frame_equal(result, expected)
 
-        # GH7192
+        # GH7192: Note we need a large number of rows to ensure this
+        #  goes through the numexpr path
         df = DataFrame(dict(A=np.random.randn(25000)))
         df.iloc[0:5] = np.nan
         expected = 1 - np.isnan(df.iloc[0:25])