Question

Using elementary transformations , find the inverse of each of the matrices,
$\left[\begin{array}{cc}1& 3\\ 2& 7\end{array}\right]$

Answer 1

$A=IA$ [row transformation]
$\left[\begin{array}{cc}1& 3\\ 2& 7\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]A$
$R_2\to R_2-2R_1$
$\left[\begin{array}{cc}1& 3\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}1& 0\\ -2& 1\end{array}\right]A$
$R_1\to R_1-3R_2$
$\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]=\left[\begin{array}{cc}7& -3\\ -2& 1\end{array}\right]A$
$\therefore A^{-1}=\left[\begin{array}{cc}7& -3\\ -2& 1\end{array}\right]$