# Homework Help: Determinant Proof Help Please

1. Nov 18, 2012

### bmb2009

1. The problem statement, all variables and given/known data

A square (nn) matrix is called skew-symmetric (or antisymmetric) if AT =
-A. Prove that if A is skew-symmetric and n is odd, then detA = 0. Is this true
for even n?

2. Relevant equations
Det(A) = Det(AT) where AT= the transpose of matrix A

3. The attempt at a solution
I started to try and say that since AT=-A then Det(AT) = Det(-A) so Det(A) = Det(-A) b/c the law that Det(A)=Det(AT) but I didnt know where to go from here.. specifically what impact does the odd number of n have to do with anything.. Any help

2. Nov 18, 2012

### bmb2009

and I assume that I need to say that Det(-A) = -Det(A) for the odd number on n so then I could conclude 2Det(A)=0 but i don't see why: Det(-A) = -Det(A) is true for odd number n matrices

3. Nov 18, 2012

### micromass

You can easily calculate det(-I), no?? (where I is the identity matrix)
Then you can write det(-A)= det((-I)A).