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.
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.
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?