Question

Let matrix $A=\left[\begin{array}{cc}1& 2\\ -3& -5\end{array}\right].$ Then inverse of matrix $A$ is

• A. $\left[\begin{array}{cc}3& 1\\ -5& -2\end{array}\right]$
• B. $\left[\begin{array}{cc}-5& -2\\ 3& 1\end{array}\right]$
• C. $\left[\begin{array}{cc}-5& 1\\ 3& -2\end{array}\right]$
• D. $\left[\begin{array}{cc}5& 2\\ -3& -1\end{array}\right]$

Answer 1

The correct option is B $\left[\begin{array}{cc}-5& -2\\ 3& 1\end{array}\right]$

Given : $A=\left[\begin{array}{cc}1& 2\\ -3& -5\end{array}\right]$
$\Rightarrow \text{Adj}\left(A\right)=\left[\begin{array}{cc}-5& -2\\ 3& 1\end{array}\right]$
and $\text{det}\left(A\right)=-5+6=1$
So, $A^{-1}=\frac{\text{Adj}\left(A\right)}{|A|}=\left[\begin{array}{cc}-5& -2\\ 3& 1\end{array}\right]$