The inverse of the matrix [ ll -1 & 5 -3 & 2 ] is - Vidyadip

MCQ

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

A
$\frac{1}{13}\left[\begin{array}{ll}2 & -5 \\ 3 & -1\end{array}\right]$
B
$\frac{1}{13}\left[\begin{array}{ll}-1 & 5 \\ -3 & 2\end{array}\right]$
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

(A) $1 / 13\left[\begin{array}{ll}2 & -5 \\ 3 & -1\end{array}\right]$
$|A|=-2+15=13$
$A^{-1}=\frac{\operatorname{adj} A}{|A|}=\frac{\left[\begin{array}{lr}2 & -5 \\ 3 & -1\end{array}\right]}{13}$
$A^{-1}=\frac{1}{13}\left[\begin{array}{ll}2 & -5 \\ 3 & -1\end{array}\right]$

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