Let A denote the 2x2 matrix with $\displaystyle a_{11} = 2, a_{12} = 0, a_{21} = 4$ and $\displaystyle a_{22} = 1$. Find a polynomial p(x) with degree two such that p(A) = 0

How can I find this one?

And how can I prove that$\displaystyle (A+B)^2 = A^2 + 2AB + B^2$ and $\displaystyle (A-B)(A+B) = A^2 - B^2$, if A and B are square matrices of the same size.

Thank you.