Suppose that $A$ is an $n \times n$ matrix and that for all $B$ of size $n \times n$, $AB=BA$. My question is why is $A$ of the form $A=CI$ where $C$ is a scalar and $I$ is the identity matrix?
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1See e.g. https://math.stackexchange.com/questions/1120202/matrices-that-commute-with-all-matrices or https://math.stackexchange.com/questions/27808/a-linear-operator-commuting-with-all-such-operators-is-a-scalar-multiple-of-the – Minus One-Twelfth May 16 '20 at 04:11
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2Does this answer your question? Properties of matrix A where AB=BA? – algae May 16 '20 at 04:14
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Thank you these sources were helpful – lambdaepsilon May 30 '20 at 05:26