The multiplicative inverse of matrix A= [ ll 2 & 1 7 & 4 ] is - Vidyadip

MCQ

The multiplicative inverse of matrix $A=\left[\begin{array}{ll}2 & 1 \\ 7 & 4\end{array}\right]$ is

A
$\left[\begin{array}{cc}4 & -1 \\ -7 & -2\end{array}\right]$
B
$\left[\begin{array}{cc}-4 & -1 \\ 7 & -2\end{array}\right]$
C
$\left[\begin{array}{cc}4 & -7 \\ 7 & 2\end{array}\right]$
✓
$\left[\begin{array}{cc}4 & -1 \\ -7 & 2\end{array}\right]$

✓

Answer

Correct option: D.

$\left[\begin{array}{cc}4 & -1 \\ -7 & 2\end{array}\right]$

(D) The multiplicative inverse of $A = A ^{-1}$
$|A|=\left|\begin{array}{ll}2 & 1 \\ 7 & 4\end{array}\right|=1 \neq 0$
$\operatorname{adj} A=\left[\begin{array}{cc}4 & -1 \\ -7 & 2\end{array}\right]$
$\therefore \quad A ^{-1}=\frac{1}{|A|} \cdot \operatorname{adj} A =\left[\begin{array}{cc}4 & -1 \\ -7 & 2\end{array}\right]$
Alternate Method:
Using Shortcut 2,
$\begin{aligned} A ^{-1} & =\frac{1}{1}\left[\begin{array}{cc}4 & -1 \\ -7 & 2\end{array}\right] \\ & =\left[\begin{array}{cc}4 & -1 \\ -7 & 2\end{array}\right]\end{aligned}$

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