Permutation/Sign via inversions/Fact

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