Chapter 8.4, Problem 5PE

To determine

To calculate: The product of the matrix $AB$, $BA$ where, $A=\left[\begin{array}{cc}-2& 1\\ \frac{3}{2}& -\frac{1}{2}\end{array}\right],B=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$ and also find the matrix $B$ is the multiplicative inverse of matrix $A$.