I have task sound like:
Examine that $ W $ is a subspace of the vector space $M_{3x3} $
$W=({A:A^t=-A}) $
To check it from definition I have to check two conditions.
1) $ \vec u + \vec v \in W $
2) $ \alpha \cdot \vec u \in W $
1) $B, C $ are matrix 3x3 and $\in W $
$B^t+C^t =(B+C)^t = -A $ and i don't know what i can do next. Could anyone tell me how i can do this task?