\(6+\frac{1}{32}-2\sqrt2\)
\(2+\frac{1}{96}-\frac{2\sqrt2}{3}\)
\(\frac{2\sqrt2}{3}\)
The correct answer is (A) : \(\frac{2\sqrt2}{3}\)
Let \( S = \left\{ m \in \mathbb{Z} : A^m + A^m = 3I - A^{-6} \right\} \), where
\[ A = \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix} \]Then \( n(S) \) is equal to ______.