Chapter 1.6, Problem 12E

Positive integral powers of a square matrix are defined by $A^1=A$ and $A^{n+1}=A^n\cdot A$ for every positive integer $n$. Evaluate $\left(A-B\right)\left(A+B\right)$ and $A^2-B^2$ and compare the results for $A=\left[\begin{array}{cc}1& 2\\ 4& 0\end{array}\right]$ and $B=\left[\begin{array}{cc}3& -1\\ 2& 1\end{array}\right]$.