Chapter 2.5, Problem 9P

Explanation of Solution

Inverse of the matrix AB:

The matrix AB and its inverse will have the property given below:

${(AB)}^{-1}AB=I$

Now, by post multiplying the expression with $B^{-1}$, the following expression is obtained,

$\begin{array}{l}{(AB)}^{-1}AB{B}^{-1}=I{B}^{-1}\\ {(AB)}^{-1}A=B^{-1}\end{array}$

Now, by post multiplying the expression with ${}^{}$