Molecules that exhibit hydrogen bonding:
\[\text{CH}_3\text{OH}, \, \text{H}_2\text{O}, \, \text{HF}, \, \text{NH}_3, \, \text{C}_6\text{H}_5\text{NO}_2\]
Benzene (C$_6$H$_6$) does not form hydrogen bonds. Total number of molecules exhibiting hydrogen bonding:
\[5\]
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 ______.