Given that $A^{-1} = \frac{1}{7} \begin{bmatrix} 2 & 1 \\ -3 & 2 \end{bmatrix}$, matrix $A$ is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $\begin{bmatrix} 2 & -1 \\ 3 & 2 \end{bmatrix}$ ##
We know that,
$(A^{-1})^{-1} = A$
Given, $A^{-1} = \begin{bmatrix} \frac{2}{7} & \frac{1}{7} \\ \frac{-3}{7} & \frac{2}{7} \end{bmatrix}$
$\Rightarrow A = \frac{\text{adj}(A^{-1})}{|A^{-1}|}$
$\Rightarrow A = \begin{bmatrix} 2 & -1 \\ 3 & 2 \end{bmatrix}$