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Mathematics Question on Adjoint and Inverse of a Matrix

If ∣A∣=3|A|=3 and A−1=[3−1\[0.3em]−5323\[0.3em]]A^{-1}=\begin{bmatrix} 3 &-1 \\\[0.3em] \frac{-5}{3} & \frac{2}{3} \\\[0.3em] \end{bmatrix} then adj AA is

A

[93\[0.3em]52]\begin{bmatrix} 9 & 3 \\\[0.3em] 5 &2 \end{bmatrix}

B

[−93\[0.3em]−52]\begin{bmatrix} -9 & 3 \\\[0.3em] -5 &2 \end{bmatrix}

C

[9−3\[0.3em]−52]\begin{bmatrix} 9 & -3 \\\[0.3em] -5 &2 \end{bmatrix}

D

[−93\[0.3em]5−2]\begin{bmatrix} -9 & 3 \\\[0.3em] 5 &-2 \end{bmatrix}

Answer

[9−3\[0.3em]−52]\begin{bmatrix} 9 & -3 \\\[0.3em] -5 &2 \end{bmatrix}

Explanation

Solution

The correct option is (C): [9−3\[0.3em]−52]\begin{bmatrix} 9 & -3 \\\[0.3em] -5 &2 \end{bmatrix}