Matrices And Determinants

Let $A=\left[\begin{array}{lll}2 & 1 & 1 \\ 0 & 1 & 0 \\ 1 & 1 & 2\end{array}\right]$. If $A^{-1}=\alpha A^2+\beta A+\gamma I$, where $\alpha, \beta$ and $\gamma$ are real numbers and $I$ is a $3 \times 3$ identity matrix, then $17 \alpha+5 \beta+\gamma=$