The inverse of the matrix [ cc 1 & -1 2 & 3 ] is ...... - Vidyadip

MCQ

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

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

✓

Answer

(B) $\frac{1}{5}\left[\begin{array}{cc}3 & 1 \\ -2 & 1\end{array}\right]$
if $A=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]$, then $A^{-1}=\frac{1}{a d-b c}\left[\begin{array}{cc}d & -b \\ -c & a\end{array}\right]$
$\therefore A=\frac{1}{5}\left[\begin{array}{cc}3 & 1 \\ -2 & 1\end{array}\right]$

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