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?
False. It is only true if $\displaystyle n$ is odd. For $\displaystyle n$ even, take:
$\displaystyle A=\begin{bmatrix}{0}&{1}\\{-1}&{0}\end{bmatrix}$
False. It is true if $\displaystyle AB=BA$. Try to find a counterexample.2.if A B are simetric then AB is simetric too
Regards.