Let $B$ be an $n$ by $r$ matrix and let $M$ be the block matrix: \begin{pmatrix} 0 &B\\ B^t & 0 \end{pmatrix}
$M$ has nullity 1. Show that the difference between the number of rows and columns of $B$ is 1.
I am supposed to use the fact that row rank = column rank for matrices over R, however I have no idea where to start.