If f is a characteristic polynomial of $A$, then $f(A)=0$.

Question

As we know, The characteristic polynomial $f$ of a binary matrix $A\in M_m(F_2)$ is defined as $f(x) = |xI + A| \in F_2[x]$. And I saw a lemma from a cryptography paper that If $f$ is a characteristic polynomial of $A \in M_m(F_2)$, then $f(A) = 0$. But $x$ is a vector and A is a matrix. Why there is $f(A)$?