Question

If $A=$ $\left(\begin{array}{cc}2& 5a\\ -3& 1\end{array}\right)$ and $A$ doesn't have multiplicative inverse, then find $A$.

Answer 1

$\therefore |A|=0\Rightarrow \left|\begin{array}{cc}2& 5a\\ -3& 1\end{array}\right|=0$
$=2\times 1-5a(-3)=0$
$\Rightarrow 2+15a=0$
$\Rightarrow a=-2/15$