Let $A: \mathbb{R}^n \rightarrow \mathbb{R}^n$ a linear transformation, and let A' be its hilbert adjoint.
Is it true that \det(A) = \det(A')?
Trying to prove:
A A' = I in $\mathbb{R}^n \ \Rightarrow \ \det(A) = \pm 1$.
Since AA' = I we have \det(I) = \det(AA') = \det(A)\det(A'), and if they're equal, then I have the result.
Thanks in advance.