Permutation matrix/Determinant is sign/Exercise

Let ${}M=\{1,\ldots ,n\}$ and let ${}\pi$ be a permutation on ${}M$. The corresponding permutation matrix ${}M_{\pi }$ is given by

${}a_{\pi (i),i}=1\,,$

all other entries being ${}0$. Show that

${}\det M_{\pi }=\operatorname {sgn} (\pi )\,.$

Create a solution