Question

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

• 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)

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

formula to find the inverse of the matrix $=A=\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)$

hence $A^{-1}=\frac{1}{ad-bc}\left(\begin{array}{cc}d& -b\\ -c& a\end{array}\right)$

in this $A=\left(\begin{array}{cc}2& 1\\ 1& 3\end{array}\right)$

$A^{-1}=\frac{1}{2\times 3-1\times 1}\left(\begin{array}{cc}3& -1\\ -1& 2\end{array}\right)$

$\therefore A^{-1}=\frac{1}{5}\left(\begin{array}{cc}3& -1\\ -1& 2\end{array}\right)$.