JEE Math Practice Question

Let $\mathrm{A}=\left[\begin{array}{cc}\alpha & -1 \\ 6 & \beta\end{array}\right], \alpha>0$, such that $\operatorname{det}(\mathrm{A})=0$ and $\alpha+\beta=1$. If I denotes $2 \times 2$ identity matrix, then the matrix $(I+A)^8$ is :

1. A.$\left[\begin{array}{cc}257 & -64 \\ 514 & -127\end{array}\right]$
2. B.$\left[\begin{array}{cc}766 & -255 \\ 1530 & -509\end{array}\right]$
3. C.$\left[\begin{array}{cc}1025 & -511 \\ 2024 & -1024\end{array}\right]$
4. D.$\left[\begin{array}{ll}4 & -1 \\ 6 & -1\end{array}\right]$