Sign of permutation and determinant

**TheFangel** · May 18th 2010, 01:35 PM

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 $sign(\pi) = det(P)$ .

**dwsmith** · May 18th 2010, 02:23 PM

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

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