I have to prove the following:
If A is an nxn skew symmetric matrix, and n is odd, show A is singular.
I have some kind of idea on how to solve it, but I'm still missing some steps.
Here are my steps.
$Det(A^T) = Det(-A)$
Then here I have to show that $det(A^T)=det(A)$ Since you switch rows and columns when taking the transpose, the determinant will clearly be the same, but I don't know how to properly show this.
Once I have shown $det(A^T)=det(A)$ I'll get:
And from here on I also don't know how to continue.
To prove that A is nonsingular for odd n I know I have to show that det(A) for odd n is zero, but I don't know how
Thanks in advance :)