## Degree of minimal polynomial

I am having trouble with this problem, appreciate some direction:

Let $A\in M^{F}_{n}$ be a matrix, and let $P(x)\in F[x]$ be a polynomial. Show that $degm_{A}(x)\geq degm_{P(A)}(x)$.

( $degm_{B}(x)$ is the degree of the minimal polynomial of matrix $B$).