Hello move123,

First your definition is incorrect. A matrix is skew symmetric if

First we know that a matrix and its transpose have the same determinant. This gives

Since the determinant function is multi-linear when we factor an number out of an n by n matrix it will have the power n e.g

when A is an n by n matrix.

using this on the first equation gives

This gives

Now what can we say about the determinant when n is odd?