Question

The inverse of the matrix $\left[\begin{array}{cc}5& -2\\ 3& 1\end{array}\right]$ is

• A. $\frac{1}{11}\left[\begin{array}{cc}1& 2\\ -3& 5\end{array}\right]$
• B. $\left[\begin{array}{cc}1& 2\\ -3& 5\end{array}\right]$
• C. $\frac{1}{13}\left[\begin{array}{cc}-2& 5\\ 1& 3\end{array}\right]$
• D. $\left[\begin{array}{cc}1& 3\\ -2& 5\end{array}\right]$

Answer 1

The correct option is A $\frac{1}{11}\left[\begin{array}{cc}1& 2\\ -3& 5\end{array}\right]$

$\begin{array}{c}A=\left[\begin{array}{c}5-2\\ 31\end{array}\right]\\ \left|A\right|=5+6=11\ne 0\\ so,Aisnon-\sin gular,A^{-1}isexist\\ so,m{A}_{11}=1,A_{12}=-3,A_{21}=2,A_{22}=5\\ A=\left(\begin{array}{cc}1& -3\\ 2& 5\end{array}\right)\Rightarrow AdjA=\left(\begin{array}{cc}1& 2\\ -3& 5\end{array}\right)\\ A^{-1}=\frac{1}{\left|A\right|}adjA\Rightarrow \frac{1}{11}\left(\begin{array}{cc}1& 2\\ -3& 5\end{array}\right)\end{array}$

Hence, this is the answer.