Let
$$M = \begin{bmatrix}0 & 1 & a \\1 & 2 & 3 \\3 & b & 1 \end{bmatrix}$$ and $$adj M = \begin{bmatrix}-1 & 1 & -1 \\8 & -6 & 2 \\-5 & 3 & -1 \end{bmatrix}$$
where a and b are real numbers. Which of the following options is/are correct?

A

a + b = 3

B

$$(adj M)^{-1} + adj M^{-1} = -M$$

C

$$det(adj M^2) = 81$$

D

If M $$\begin{bmatrix}\alpha \\ \beta \\ \gamma \end{bmatrix} = \begin{bmatrix}1 \\2 \\3 \end{bmatrix},$$ then $$\alpha - \beta + \gamma = 3$$