Hi,

I have this proof that I can't really show, can someone help me out?

Prove that, if $\displaystyle P \in R^{n,n}$ represents the permutation $\displaystyle \pi \in S_n$ of columns, i.e. $\displaystyle PA = (a_{\pi(1)},...,a_{\pi(n)})$, then we have $\displaystyle sign(\pi) = det(P)$.