A square matrix A is called skew-symmetric if A^T= A. Prove that if A is a skew-symmetric n x nmatrix and n is odd, then A is not inveritible.

what if n is even ?

Please help, I have no idea what is talking about.

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- March 20th 2011, 08:32 AMmove123A square matrix A is called skew-symmetric
A square matrix A is called skew-symmetric if A^T= A. Prove that if A is a skew-symmetric n x nmatrix and n is odd, then A is not inveritible.

what if n is even ?

Please help, I have no idea what is talking about. - March 20th 2011, 09:18 AMTheEmptySet
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? - March 20th 2011, 09:53 AMFernandoRevilla
- March 20th 2011, 10:50 AMmove123
- March 20th 2011, 12:08 PMFernandoRevilla