01 - General Commutative Matrix

General Commutative Matrix

Let $A$ be an $n\times n$ matrix such that $AM=MA$ for all $n\times n$ matrices M (i.e. commutes with all $n\times n$ matrices)

Then $A=\lambda I_n$ for some $\lambda \in \mathbb{R}$

Proof - TODO

TODO: write up