Suppose that $A$ is an $n\times n$ matrix and $I_m$ is an $m-$dimensional identity matrix. If $[A\otimes I_m,B]=0$ for all $A$ where $\otimes$ is Kronecker product, does it imply $B$ must be of form $B=I_n\otimes C$ where $C$ is an $m\times m$ matrix? If so, how to prove it?

  • $\begingroup$ Is the bracket for commutator ? $\endgroup$
    – dezdichado
    Mar 18 at 22:35
  • $\begingroup$ Yes @dezdichado $\endgroup$
    – ZHC
    Mar 19 at 9:48


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