diff --git a/src/ArrayInterface.jl b/src/ArrayInterface.jl
index dd6123810..5f07f6da3 100644
--- a/src/ArrayInterface.jl
+++ b/src/ArrayInterface.jl
@@ -50,6 +50,8 @@ Query whether an array type has fast scalar indexing
 """
 fast_scalar_indexing(x) = true
 fast_scalar_indexing(x::AbstractArray) = fast_scalar_indexing(typeof(x))
+fast_scalar_indexing(::Type{<:LinearAlgebra.AbstractQ}) = false
+fast_scalar_indexing(::Type{<:LinearAlgebra.LQPackedQ}) = false
 
 """
     allowed_getindex(x,i...)
diff --git a/test/runtests.jl b/test/runtests.jl
index c5979f4d0..c77bf0527 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,6 +1,6 @@
 using ArrayInterface, Test
 using Base: setindex
-import ArrayInterface: has_sparsestruct, findstructralnz
+import ArrayInterface: has_sparsestruct, findstructralnz, fast_scalar_indexing
 @test ArrayInterface.ismutable(rand(3))
 
 using StaticArrays
@@ -39,6 +39,10 @@ Sp=sparse([1,2,3],[1,2,3],[1,2,3])
 rowind,colind=findstructralnz(Sp)
 @test [Tri[rowind[i],colind[i]] for i in 1:length(rowind)]==[1,2,3]
 
+@test !fast_scalar_indexing(qr(rand(10, 10)).Q)
+@test !fast_scalar_indexing(qr(rand(10, 10), Val(true)).Q)
+@test !fast_scalar_indexing(lq(rand(10, 10)).Q)
+
 using BandedMatrices
 
 B=BandedMatrix(Ones(5,5), (-1,2))