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I was thinking about the following problem:
Let $A$ be an $n\times n$ matrix over real numbers such that $AB=BA,$ for all $n\times n$ matrices $B$.Then which of the following options is correct?
(a)$A$ must be zero,
(b)$A$ must be the identity,
(c)$A$ must be a diagonal matrix,
(d)$A$ must be either $0$ or the identity.
I think the answer will be between $(c)$ and $(d)$. But i am not sure how to get the exact result.Can someone show me the right direction? Thanks in advance for your time.