Vector space/Endomorphism/Invariant linear subspace/Polynomial/Exercise

Let ${}K$ be a field, let ${}V$ be a ${}K$-vector space, and let

$\varphi \colon V\longrightarrow V$

a linear mapping. Let ${}U\subseteq V$ be a ${}\varphi$-invariant linear subspace of ${}V$. Show that, for a polynomial ${}P\in K[X]$, the space ${}U$ is also ${}P(\varphi )$-invariant.

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