Let $F$ be a field and $G = \mathrm{GL}_n(F)$. For $g \in G$, write $C_g = \{hgh^{-1} \mid h \in G\}$. Let $X = \{C_g \mid g \in G,\ \text{the order of } g \text{ is } 2\}$. Determine $|X|$.
Let $F$ be a field and $G = \mathrm{GL}_n(F)$. For $g \in G$, write $C_g = \{hgh^{-1} \mid h \in G\}$. Let $X = \{C_g \mid g \in G,\ \text{the order of } g \text{ is } 2\}$. Determine $|X|$.