Given A is a linear transformation find a non zero polynomial such that p(A)=0

Question

Here $x_0$ is a fixed vector and $y_0$ is any linear functional.

(a) The space of all linear transformations $V \to V$ has dimension $n^2$. Consider $I,A,A^2,A^3,.....A^{n^2}$. Then this collection forms a linearly dependent set. So we have a non trivial relation amongst these which will give us a polynomial such that $p(A)=0$.

(b) Don't know how to proceed.