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Let $A$ and $B$ be $n \times n$ matrices with $A B=0$. Give a proof or counterexample for each of the following.

a) Either $A=0$ or $B=0$ (or both).
b) $B A=0$
c) If $\operatorname{det} A=-3$, then $B=0$.
d) If $B$ is invertible then $A=0$.
e) There is a vector $V \neq 0$ such that $B A V=0$.
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