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

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

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