Let $A$, $B$, $C$ and $D$ be square matrices $n\times n$ over $ \mathbb{R} $
.
Assume that $AB^T$ and $CD^T$ are symmetric ( so $AB^T=A^TB$ and$CD^T=C^TD$ )
and $AD^T-BC^T=I$
Prove that: $A^TD-C^TB=I$
$T$ means transpose
$I$ is identity matrix
I need some advice, maybe there is some trick with trace of an matricx.
