Based on biomolecules theory and the structure of the named compounds:
\(\alpha\)-Glucose and \(\alpha\)-Galactose are epimers, differing in configuration around one specific carbon atom.
\(\alpha\)-Glucose and \(\beta\)-Glucose are anomers, differing at the anomeric carbon.
\(\alpha\)-Glucose and \(\alpha\)-Fructose are functional isomers, as they have different functional groups.
\(\alpha\)-Glucose and \(\alpha\)-Ribose are from different homologous series.
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 ______.
Let \( T_r \) be the \( r^{\text{th}} \) term of an A.P. If for some \( m \), \( T_m = \dfrac{1}{25} \), \( T_{25} = \dfrac{1}{20} \), and \( \displaystyle\sum_{r=1}^{25} T_r = 13 \), then \( 5m \displaystyle\sum_{r=m}^{2m} T_r \) is equal to: