Consider the matrix \(A = \begin{pmatrix} 2 & 1\\ 1 & 2 \end{pmatrix} \)
Let \( A^n \) represent the matrix A raised to the power n . If \(\lambda_1 \) and \(\lambda_2 \) are the eigenvalues of A , and \(A^8 \) satisfies:
\(A^8 = \begin{pmatrix} x & y \\ z & w \end{pmatrix} \)
where x, y, z, w are constants, then the trace of \(A^8 \) is:
1
6561
2
6560
3
6563
4
6562