Formaldehyde (HCHO) is the most reactive towards nucleophilic addition reactions because:
• It has no alkyl groups attached to the carbonyl carbon, leading to the lowest steric hindrance at the carbonyl carbon.
• The partial positive charge on the carbonyl carbon is highest due to the absence of electron-donating groups (alkyl groups), making it highly electrophilic.
Thus, HCHO is the most reactive aldehyde for nucleophilic addition reactions.
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 ______.