Let \( M=\left[\begin{array}{lll}0 & 1 & a \\ 1 & 2 & 3 \\ 3 & b & 1\end{array}\right] \) and ad...

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Let \( M=\left[\begin{array}{lll}0 & 1 & a \\ 1 & 2 & 3 \\ 3 & b & 1\end{array}\right] \) and adj \( M=\left[\begin{array}{ccc}-1 & 1 & -1 \\ 8 & -6 & 2 \\ -5 & 3 & -1\end{array}\right] \)\( \mathrm{PW} \)where \( a \) and \( b \) are real numbers. Which of the following options is/are correct ?(A) \( \operatorname{det}\left(\right. \) adj \( \left.M^{2}\right)=81 \)(B) \( a+b=3 \)-(C) If \( M\left[\begin{array}{l}\alpha \\ \beta \\ \gamma\end{array}\right]=\left[\begin{array}{l}1 \\ 2 \\ 3\end{array}\right] \), then \( \alpha-\beta+\gamma=3 \)(D) \( (\text { adj } M)^{-1}+ \) adj \( M^{-1}=-M \)
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