Question

Convert $\left[\begin{array}{cc}1& -1\\ 2& 3\end{array}\right]$ into an identity matrix by sutaible raw transformation

Answer 1

$A=\left[\begin{array}{cc}1& -1\\ 2& 3\end{array}\right]$
Coverting into Identity matrix
$I=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$
$R_2\to R_2-2R_1$
$\left[\begin{array}{cc}1& -1\\ 2-2\left(1\right)& 3-2(-1)\end{array}\right]$
$\left[\begin{array}{cc}1& -1\\ 0& 5\end{array}\right]$
$R_2\to \frac{R_2}{5}$
$\left[\begin{array}{cc}1& -1\\ 0& \frac{5}{5}\end{array}\right]$
$\left[\begin{array}{cc}1& -1\\ 0& 1\end{array}\right]$
Now, $R_1\to R_1+R_2$
$\left[\begin{array}{cc}1+0& -1+1\\ 0& 1\end{array}\right]$
$\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$