## Question

###### Let $A$ be an $n imes n$ (square) matrix. Prove the following two statements:(a) If $A$ is invertible and $A B=0$ for some $n imes n$ matrix $B$, then $B=0$.(b) If $A$ is not invertible, then there exists an $n imes n$ matrix $B$ such that $A B=0$ but $B eq 0$

Let $A$ be an $n imes n$ (square) matrix. Prove the following two statements: (a) If $A$ is invertible and $A B=0$ for some $n imes n$ matrix $B$, then $B=0$. (b) If $A$ is not invertible, then there exists an $n imes n$ matrix $B$ such that $A B=0$ but $B eq 0$

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