Let A be a 3 × 3 real matrix such that A^2(A-2 I)-4(A-I)=O, where I and O are the identity and null matrices, respectively. If A^5=α A^2+β A +γ I,…

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