Permutation matrix/Orientation-preserving/Exercise

Let ${}M=\{1,\ldots ,n\}$, let ${}\pi$ be a permutation on ${}M$, and let ${}M_{\pi }$ denote the corresponding permutation matrix. Show that ${}M$ is orientation-preserving if and only if

${}\operatorname {sgn} (\pi )=1\,$

holds.

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