Question

Find inverse, by elementary row operations (if possible), of the following matrices
$\left[\begin{array}{cc}1& -3\\ -2& 6\end{array}\right]$

Answer 1

To check if the inverse exist we find the determinant:

We have:

$A=\left[\begin{array}{cc}1& -3\\ -2& 6\end{array}\right]$

So, $\left|A\right|=1\times 6-(-2\times -3)$

$\Rightarrow \left|A\right|=6-6=0$

Since, $|A|=0$, hence the inverse does not exist