# Thread: Sign of permutation and determinant

1. ## Sign of permutation and determinant

Hi,

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

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

2. Originally Posted by TheFangel
Hi,

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

Prove that, if $P \in R^{n,n}$ represents the permutation $\pi \in S_n$ of columns, i.e. $PA = (a_{\pi(1)},...,a_{\pi(n)})$, then we have $sign(\pi) = det(P)$.
I don't have a good proof of this but that method becomes too difficult when you are using matrices greater than 3x3