diff --git a/src/host/mapreduce.jl b/src/host/mapreduce.jl
index 32520ebc..c589a3de 100644
--- a/src/host/mapreduce.jl
+++ b/src/host/mapreduce.jl
@@ -10,6 +10,30 @@ mapreducedim!(f, op, R::AnyGPUArray, A::AbstractArrayOrBroadcasted;
 Base.mapreducedim!(f, op, R::AnyGPUArray, A::AbstractArray) = mapreducedim!(f, op, R, A)
 Base.mapreducedim!(f, op, R::AnyGPUArray, A::Broadcast.Broadcasted) = mapreducedim!(f, op, R, A)
 
+# resolve ambiguities with Adjoint/Transpose
+# https://github.com/JuliaLang/julia/blob/master/stdlib/LinearAlgebra/src/adjtrans.jl#L440-L448
+Base.mapreducedim!(f, op::LinearAlgebra.CommutativeOps, B::AnyGPUArray, A::LinearAlgebra.TransposeAbsMat) =
+    (Base.mapreducedim!(f∘transpose, op, LinearAlgebra.switch_dim12(B), parent(A)); B)
+Base.mapreducedim!(f, op::LinearAlgebra.CommutativeOps, B::AnyGPUArray, A::LinearAlgebra.AdjointAbsMat) =
+    (Base.mapreducedim!(f∘adjoint, op, LinearAlgebra.switch_dim12(B), parent(A)); B)
+Base.mapreducedim!(f::typeof(identity), op::Union{typeof(*),typeof(Base.mul_prod)}, B::AnyGPUArray, A::LinearAlgebra.TransposeAbsMat{<:Union{Real,Complex}}) =
+    (Base.mapreducedim!(f∘transpose, op, LinearAlgebra.switch_dim12(B), parent(A)); B)
+Base.mapreducedim!(f::typeof(identity), op::Union{typeof(*),typeof(Base.mul_prod)}, B::AnyGPUArray, A::LinearAlgebra.AdjointAbsMat{<:Union{Real,Complex}}) =
+    (Base.mapreducedim!(f∘adjoint, op, LinearAlgebra.switch_dim12(B), parent(A)); B)
+
+# resolve ambiguities with PermutedDimsArray
+# https://github.com/JuliaLang/julia/blob/master/base/permuteddimsarray.jl#L355-L364
+function Base.mapreducedim!(f, op::LinearAlgebra.CommutativeOps, B::AnyGPUArray{T,N}, A::PermutedDimsArray{S,N,perm,iperm}) where {T,S,N,perm,iperm}
+    C = PermutedDimsArray{T,N,iperm,perm,typeof(B)}(B) # make the inverse permutation for the output
+    Base.mapreducedim!(f, op, C, parent(A))
+    B
+end
+function Base.mapreducedim!(f::typeof(identity), op::Union{typeof(Base.mul_prod),typeof(*)}, B::AnyGPUArray{T,N}, A::PermutedDimsArray{<:Union{Real,Complex},N,perm,iperm}) where {T,N,perm,iperm}
+    C = PermutedDimsArray{T,N,iperm,perm,typeof(B)}(B) # make the inverse permutation for the output
+    Base.mapreducedim!(f, op, C, parent(A))
+    B
+end
+
 neutral_element(op, T) =
     error("""GPUArrays.jl needs to know the neutral element for your operator `$op`.
              Please pass it as an explicit argument to `GPUArrays.mapreducedim!`,