If $\mathrm{A}=\left[\begin{array}{cc}2 & -2 \\ 4 & 3\end{array}\right]$, then $\mathrm{A}^{-1}=$

If $\mathrm{A}=\left[\begin{array}{cc}2 & -2 \\ 4 & 3\end{array}\right]$, then $\mathrm{A}^{-1}=$
  1. $\quad-\frac{1}{2}\left[\begin{array}{cc}3 & 2 \\ -4 & 2\end{array}\right]$
  2. $\frac{1}{14}\left[\begin{array}{cc}3 & 2 \\ -4 & 2\end{array}\right]$
  3. $\frac{1}{14}\left[\begin{array}{cc}-3 & -2 \\ 4 & -2\end{array}\right]$
  4. $\quad-\frac{1}{14}\left[\begin{array}{ll}3 & -2 \\ 4 & -2\end{array}\right]$

Solution

$\begin{aligned} A & =\left[\begin{array}{cc}2 & -2 \\ 4 & 3\end{array}\right] \\ & A^{-1}=\frac{1}{|A|} \operatorname{Adj} A \\ \therefore \quad A^{-1} & =\frac{1}{14}\left[\begin{array}{cc}3 & 2 \\ -4 & 2\end{array}\right]\end{aligned}$

Asked in: MHT CET 2024 (03 May Shift 1)

Practice more Matrices questions on Aicharya