If A= [ cc 3 & 1 -1 & 2 ], then find A^ -1 . - Vidyadip

MCQ

If $A=\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]$, then find $A^{-1}$.

✓
$\frac{1}{7}\left[\begin{array}{cc}2 & -1 \\ 1 & 3\end{array}\right]$
B
$\frac{1}{7}\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right]$
C
$\frac{1}{7}\left[\begin{array}{cc}-2 & 1 \\ -1 & -3\end{array}\right]$
D
$\frac{1}{7}\left[\begin{array}{cc}2 & 1 \\ 1 & -3\end{array}\right]$

✓

Answer

Correct option: A.

$\frac{1}{7}\left[\begin{array}{cc}2 & -1 \\ 1 & 3\end{array}\right]$

(a) : $|A|=6+1=7 \neq 0, \therefore A^{-1}$ exists.
$\operatorname{adj} A=\left[\begin{array}{cc}2 & -1 \\ 1 & 3\end{array}\right] \quad \therefore A^{-1}=\frac{1}{7}\left[\begin{array}{cc}2 & -1 \\ 1 & 3\end{array}\right]$

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