The correct reaction involves the substitution of an alkyl halide with HI (Hydrogen iodide), which proceeds with the formation of a halide and is a typical example of nucleophilic substitution. This reaction follows Markovnikov’s addition rule where the halide (in this case, iodine) adds to the more substituted carbon of the alkyl halide.
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 ______.