diff --git a/src/abstract.jl b/src/abstract.jl
index a08bd63..c3940a3 100644
--- a/src/abstract.jl
+++ b/src/abstract.jl
@@ -174,6 +174,11 @@ storage_type(op::AbstractLinearOperator) = error("please implement storage_type
 storage_type(op::LinearOperator) = typeof(op.Mv5)
 storage_type(M::AbstractMatrix{T}) where {T} = Vector{T}
 
+# Lazy wrappers
+storage_type(op::Adjoint) = storage_type(parent(op))
+storage_type(op::Transpose) = storage_type(parent(op))
+storage_type(op::Diagonal) = typeof(parent(op))
+
 """
   reset!(op)
 
diff --git a/test/gpu/amdgpu.jl b/test/gpu/amdgpu.jl
index bda6b90..d12f3b9 100644
--- a/test/gpu/amdgpu.jl
+++ b/test/gpu/amdgpu.jl
@@ -11,5 +11,10 @@ using LinearOperators, AMDGPU
   y = M * v
   @test y isa ROCArray{Float32}
 
+  @test LinearOperators.storage_type(A) == LinearOperators.storage_type(adjoint(A))
+  @test LinearOperators.storage_type(A) == LinearOperators.storage_type(transpose(A))
+  @test LinearOperators.storage_type(A) == LinearOperators.storage_type(adjoint(A))
+  @test LinearOperators.storage_type(Diagonal(v)) == typeof(v)
+
   @testset "AMDGPU S kwarg" test_S_kwarg(arrayType = ROCArray)
 end
diff --git a/test/gpu/nvidia.jl b/test/gpu/nvidia.jl
index c707dee..63bf732 100644
--- a/test/gpu/nvidia.jl
+++ b/test/gpu/nvidia.jl
@@ -13,5 +13,11 @@ using LinearOperators, CUDA, CUDA.CUSPARSE, CUDA.CUSOLVER
   v = CUDA.rand(35)
   y = M * v
   @test y isa CuVector{Float32}
+
+  @test LinearOperators.storage_type(A) == LinearOperators.storage_type(adjoint(A))
+  @test LinearOperators.storage_type(A) == LinearOperators.storage_type(transpose(A))
+  @test LinearOperators.storage_type(A) == LinearOperators.storage_type(adjoint(A))
+  @test LinearOperators.storage_type(Diagonal(v)) == typeof(v)
+
   @testset "Nvidia S kwarg" test_S_kwarg(arrayType = CuArray)
 end