Question

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

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

Answer 1

Answer: (B)

$\frac{1}{5}\left[\begin{array}{cc}3& -1\\ -1& 2\end{array}\right]$

Given, $A=\left[\begin{array}{cc}2& 1\\ 1& 3\end{array}\right]$
$|A|=5$
Now, $adjA=C^T={\left[\begin{array}{cc}3& -1\\ -1& 2\end{array}\right]}^T$
$\Rightarrow adjA=\left[\begin{array}{cc}3& -1\\ -1& 2\end{array}\right]$
$A^{-1}=\frac{1}{5}\left[\begin{array}{cc}3& -1\\ -1& 2\end{array}\right]$