Make inv of Adjoint and Transpose inferable and make it work when (Ju…

…liaLang#30047)

the wrapped array is complex.

Fixes JuliaLang#30038

stdlib/LinearAlgebra/src/generic.jl

@@ -799,6 +799,8 @@ function inv(A::AbstractMatrix{T}) where T
  dest = Matrix{S0}(I, n, n)
  ldiv!(factorize(convert(AbstractMatrix{S}, A)), dest)
 end
+inv(A::Adjoint) = adjoint(inv(parent(A)))
+inv(A::Transpose) = transpose(inv(parent(A)))
 
 pinv(v::AbstractVector{T}, tol::Real = real(zero(T))) where {T<:Real} = _vectorpinv(transpose, v, tol)
 pinv(v::AbstractVector{T}, tol::Real = real(zero(T))) where {T<:Complex} = _vectorpinv(adjoint, v, tol)

stdlib/LinearAlgebra/test/dense.jl

@@ -872,16 +872,13 @@ end
 @testset "inverse of Adjoint" begin
  A = randn(n, n)
 
- @test inv(A')*A' ≈ I
- @test inv(transpose(A))*transpose(A) ≈ I
+ @test @inferred(inv(A'))*A' ≈ I
+ @test @inferred(inv(transpose(A)))*transpose(A) ≈ I
 
  B = complex.(A, randn(n, n))
- B = B + transpose(B)
 
- # The following two cases fail because ldiv!(F::Adjoint/Transpose{BunchKaufman},b)
- # isn't implemented yet
- @test_broken inv(B')*B' ≈ I
- @test_broken inv(transpose(B))*transpose(B) ≈ I
+ @test @inferred(inv(B'))*B' ≈ I
+ @test @inferred(inv(transpose(B)))*transpose(B) ≈ I
 end
 
 end # module TestDense