Let $\mathbf{A}$ be a $2 \times 2$ matrix with real entries such that $\mathbf{A}' = \alpha \mathbf{A} + \mathbf{I}$, where $\alpha \in \mathbb{R} - \{-1, 1\}$. If $\det(\mathbf{A}^2 - \mathbf{A}) = 4$, then the sum of all possible values of $\alpha$ is equal to: