Examine that $W$ is a subspace of the vector space $M_{3x3}$
$W=({A:det(A) \ge} 0)$
I have two conditions:
1) $ \vec u + \vec v \in W $
2) $ \alpha \cdot \vec u \in W $
$ B,C \in W $
$det(B) + det(C) \ge 0 $
I don't know any properties of determine of matrix which could help with these.