If \(|A| = 3\) and \(A^{-1} = \begin{bmatrix} 3 & -1\\ -\displaystyle\frac{5}{3} & \displaystyle\frac{2}{3}\end{bmatrix}\) then adj A is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\begin{bmatrix} 9 & -3\\ -5 & 2\end{bmatrix}\)
The inverse through the adjoint is
\( \displaystyle A^{-1} = \frac{1}{|A|}\,\mathrm{adj}\,A \)
so
\( \mathrm{adj}\,A = |A|\,A^{-1} \)
\( = 3\begin{bmatrix} 3 & -1\\ -\displaystyle\frac{5}{3} & \displaystyle\frac{2}{3}\end{bmatrix} \)
\( = \begin{bmatrix} 9 & -3\\ -5 & 2\end{bmatrix} \)