Given a $n \times m$ permutation matrix $X$ (with $0 < n <= m$), I would like to show that $X'X$ must be diagonal and $XX'=I$. How can I prove that?
Note that a permutation matrix is a square (0, 1)-matrix, all of whose columns and rows each have exactly one nonzero element. Here, I am focussing on a non-square version in which each row has exactly one nonzero element (i.e., removing the condition on the columns).