Mathematics Question from JEE Main 2025 · 2 April, Shift 2

Let $A$ be a $3 \times 3$ real matrix such that $A^2(A - 2I) - 4(A - I) = O$, where $I$ and $O$ are the identity and null matrices, respectively. If $A^5 = \alpha A^2 + \beta A + \gamma I$, where $\alpha$, $\beta$, and $\gamma$ are real constants, then $\alpha + \beta + \gamma$ is equal to: