diff --git a/stdlib/LinearAlgebra/src/uniformscaling.jl b/stdlib/LinearAlgebra/src/uniformscaling.jl
index 71dd11a2f9e87..1b2e3010ff27d 100644
--- a/stdlib/LinearAlgebra/src/uniformscaling.jl
+++ b/stdlib/LinearAlgebra/src/uniformscaling.jl
@@ -265,7 +265,8 @@ end
 *(J::UniformScaling, x::Number) = UniformScaling(J.λ*x)
 
 /(J1::UniformScaling, J2::UniformScaling) = J2.λ == 0 ? throw(SingularException(1)) : UniformScaling(J1.λ/J2.λ)
-/(J::UniformScaling, A::AbstractMatrix) = lmul!(J.λ, inv(A))
+/(J::UniformScaling, A::AbstractMatrix) =
+    (invA = inv(A); lmul!(J.λ, convert(AbstractMatrix{promote_type(eltype(J),eltype(invA))}, invA)))
 /(A::AbstractMatrix, J::UniformScaling) = J.λ == 0 ? throw(SingularException(1)) : A/J.λ
 /(v::AbstractVector, J::UniformScaling) = reshape(v, length(v), 1) / J
 
@@ -273,7 +274,8 @@ end
 
 \(J1::UniformScaling, J2::UniformScaling) = J1.λ == 0 ? throw(SingularException(1)) : UniformScaling(J1.λ\J2.λ)
 \(J::UniformScaling, A::AbstractVecOrMat) = J.λ == 0 ? throw(SingularException(1)) : J.λ\A
-\(A::AbstractMatrix, J::UniformScaling) = rmul!(inv(A), J.λ)
+\(A::AbstractMatrix, J::UniformScaling) =
+    (invA = inv(A); rmul!(convert(AbstractMatrix{promote_type(eltype(invA),eltype(J))}, invA), J.λ))
 \(F::Factorization, J::UniformScaling) = F \ J(size(F,1))
 
 \(x::Number, J::UniformScaling) = UniformScaling(x\J.λ)
diff --git a/stdlib/LinearAlgebra/test/uniformscaling.jl b/stdlib/LinearAlgebra/test/uniformscaling.jl
index 4eea74b12ff15..33b2ba7032734 100644
--- a/stdlib/LinearAlgebra/test/uniformscaling.jl
+++ b/stdlib/LinearAlgebra/test/uniformscaling.jl
@@ -528,4 +528,12 @@ end
     @test sum(A - I) ≈ -3.0
 end
 
+@testset "type promotion when dividing UniformScaling by matrix" begin
+    A = randn(5,5)
+    cA = complex(A)
+    J = (5+2im)*I
+    @test J/A ≈ J/cA
+    @test A\J ≈ cA\J
+end
+
 end # module TestUniformscaling