Chapter 9.4, Problem 64E

(a)

To determine

To show: The expression $A\times B=B\times A=I$ that is A and B are multiplicative inverses

for any $2\times 2$ matrix where $A=\left[\begin{array}{cc}5& -2\\ -2& 1\end{array}\right]$ and $B=\left[\begin{array}{cc}1& 2\\ 2& 5\end{array}\right]$.

(b)

To determine

To show: The expression $A\times B=B\times A=I$ that is A and B are multiplicative inverses

for any $2\times 2$ matrix where $A=\left[\begin{array}{cc}7& 3\\ 2& 1\end{array}\right]$ and $B=\left[\begin{array}{cc}1& -3\\ -2& 7\end{array}\right]$.