Chapter 2.5, Problem 1P

Explanation of Solution

Inverse of the given matrix:

Consider the given matrix,

$A=\left[\begin{array}{l}13\\ 25\end{array}\right]$

Suppose that the inverse of the given matrix is as follows:

$A^{-1}=\left[\begin{array}{l}ef\\ gh\end{array}\right]$

Then, the following equations are solved,

$\left[\begin{array}{l}13\\ 25\end{array}\right]\left[\begin{array}{l}e\\ g\end{array}\right]=\left[\begin{array}{l}1\\ 0\end{array}\right]\mathrm{......}(1)$

$\left[\begin{array}{l}13\\ 25\end{array}\right]\left[\begin{array}{l}f\\ h\end{array}\right]=\left[\begin{array}{l}0\\ 1\end{array}\right]\mathrm{}$