Let $$A = \begin{bmatrix} -1 & 1 & -1 \\ 1 & 0 & 1 \\ 0 & 0 & 1 \end{bmatrix}$$ satisfy
$$A^2 + \alpha\left(\text{adj}(\text{adj}(A))\right) + \beta\left(\text{adj}(A)\left(\text{adj}(\text{adj}(A))\right)\right) = \begin{bmatrix} 2 & -2 & 2 \\ -2 & 0 & -1 \\ 0 & 0 & -1 \end{bmatrix}$$
for some $$\alpha, \beta \in \mathbb{R}$$. Then $$(\alpha - \beta)^2$$ is equal to _______.