# Math Help - simetrix matrices determinant 2

1. ## simetrix matrices determinant 2

A B are nXn order matrices
1.if A^t=-A then det A=0
2.if A B are simetric then AB is simetric too

for each one of these is it true or false?

2. Originally Posted by transgalactic
A B are nXn order matrices
1.if A^t=-A then det A=0
False. It is only true if $n$ is odd. For $n$ even, take:

$A=\begin{bmatrix}{0}&{1}\\{-1}&{0}\end{bmatrix}$

2.if A B are simetric then AB is simetric too
False. It is true if $AB=BA$. Try to find a counterexample.

Regards.