Permutation/Sign via inversions/Fact

Let ${}M=\{1,\ldots ,n\}$ and let ${}\pi$ be a permutation on ${}M$. Let ${}k={\#\left(F\right)}$ denote the number of inversions of ${}\pi$.

Then the

sign of ${}\pi$ equals

${}\operatorname {sgn} (\pi )=(-1)^{k}\,.$

Proof, Write another proof