Given a matrix $A$ and the transpose of its inverse, $A^{-T}$, are there any useful properties of their product $A^{-T}A$? The only thing that came to my mind was
$$\det(A^{-T}A) = \underbrace{\det(A^{-T})}_{=(\det A)^{-1}}\det A = 1$$
Are there any other statements that can be made about e.g. the trace or eigenvalues of this product? What about their commutator $[A^{-T},A]$?