Minimal polynomial/Factorization/Substitutions not bijective/Exercise

Let $M$ be an $n\times n$-matrix over $K$ with the minimal polynomial $P\in K[X]$. Let

$P=F_1\cdots F_k$

be a factorization into polynomials $F_i$ of positive degree. Show that $F_i(M)$ is not bijective.

Create a solution