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