Chapter 4.3, Problem 71E

To determine

Whether the inverse of matrix $\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]$ is given by ${\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]}^{-1}=\frac{1}{ad-bc}\left[\begin{array}{cc}d& -b\\ -c& a\end{array}\right]$ or not, where, $ad-bc\ne 0$ by the use of matrix multiplication.