Mathematics

Problem

Let

A = \begin{bmatrix} \alpha & -1 \\ 6 & \beta \end{bmatrix}

\alpha > 0

, such that

\det(A) = 0

and

\alpha + \beta = 1

. If I denotes

2 \times 2

identity matrix, then the matrix

(1 + A)^8

is: (1)

\begin{bmatrix} 4 & -1 \\ 6 & -1 \end{bmatrix}

(2)

\begin{bmatrix} 257 & -64 \\ 514 & -127 \end{bmatrix}

(3)

\begin{bmatrix} 1025 & -511 \\ 2024 & -1024 \end{bmatrix}

(4)

\begin{bmatrix} 766 & -255 \\ 1530 & -509 \end{bmatrix}