Question

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

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

Answer 1

The correct option is A $\frac{1}{13}\left[\begin{array}{cc}2& -5\\ 3& -1\end{array}\right]$

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

The determinant of the given matrix is $D=-2+15=13$

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

Therefore the inverse of given matrix will be $\frac{1}{13}\left[\begin{array}{cc}2& -5\\ 3& -1\end{array}\right]$