Let $A,B\in {M}_{n}(\mathbb{C})$ be matrices and $f\in \mathbb{C}[X]$ such that $Af(B)=B$. Prove that if $f(B)$ is not invertible, $f(0)=0$

Mauricio Mathis
2022-07-22
Answered

Let $A,B\in {M}_{n}(\mathbb{C})$ be matrices and $f\in \mathbb{C}[X]$ such that $Af(B)=B$. Prove that if $f(B)$ is not invertible, $f(0)=0$

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