Question

Convert $\left[\begin{array}{cc}1& -1\\ 2& 3\end{array}\right]$ into an identify matrix by suitable row transformations.

Answer 1

$R_2\to R_2-2R_1$ $\left[\begin{array}{cc}1& -1\\ 0& 5\end{array}\right]$ $R_2\to \frac{R_2}{5}$ $\left[\begin{array}{cc}1& -1\\ 0& 1\end{array}\right]$

$R_1\to R_1+R_2$ $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]\to I$.