The inverse of the matrix [ cc 3 & -2 1 & 4 ] is - Vidyadip

MCQ

The inverse of the matrix $\left[\begin{array}{cc}3 & -2 \\ 1 & 4\end{array}\right]$ is

✓
$\left[\begin{array}{cc}\frac{4}{14} & \frac{2}{14} \\ \frac{-1}{14} & \frac{3}{14}\end{array}\right]$
B
$\left[\begin{array}{cc}\frac{3}{14} & \frac{-2}{14} \\ \frac{1}{14} & \frac{4}{14}\end{array}\right]$
C
$\left[\begin{array}{cc}\frac{4}{14} & \frac{-2}{14} \\ \frac{1}{14} & \frac{3}{14}\end{array}\right]$
D
$\left[\begin{array}{cc}\frac{3}{14} & \frac{2}{14} \\ \frac{1}{14} & \frac{4}{14}\end{array}\right]$

✓

Answer

Correct option: A.

$\left[\begin{array}{cc}\frac{4}{14} & \frac{2}{14} \\ \frac{-1}{14} & \frac{3}{14}\end{array}\right]$

(A) Let $A=\left[\begin{array}{cc}3 & -2 \\ 1 & 4\end{array}\right] \Rightarrow|A|=14 \neq 0$
$\therefore \quad A ^{-1}=\frac{1}{14}\left[\begin{array}{cc}4 & 2 \\ -1 & 3\end{array}\right]=\left[\begin{array}{ll}\frac{4}{14} & \frac{2}{14} \\ \frac{-1}{14} & \frac{3}{14}\end{array}\right]$
...[Using Shortcut 2]

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