Let $k$ be a finite field of characteristic $p > 2$ and $G$ the subgroup of $\mathrm { GL } _ { 2 } ( k )$ consisting of all matrices whose first column is $\left[ \begin{array} { l } 1 \\ 0 \end{array} \right]$. Pick the correct statement(s) from below. (A) $G$ is a normal subgroup of $\mathrm { GL } _ { 2 } ( k )$. (B) $G$ is a $p$-group. (C) $\left\{ \left[ \begin{array} { l l } 1 & a \\ 0 & 1 \end{array} \right] : a \in k \right\}$ is a normal subgroup of $G$. (D) $G$ is abelian.
Let $k$ be a finite field of characteristic $p > 2$ and $G$ the subgroup of $\mathrm { GL } _ { 2 } ( k )$ consisting of all matrices whose first column is $\left[ \begin{array} { l } 1 \\ 0 \end{array} \right]$. Pick the correct statement(s) from below.\\
(A) $G$ is a normal subgroup of $\mathrm { GL } _ { 2 } ( k )$.\\
(B) $G$ is a $p$-group.\\
(C) $\left\{ \left[ \begin{array} { l l } 1 & a \\ 0 & 1 \end{array} \right] : a \in k \right\}$ is a normal subgroup of $G$.\\
(D) $G$ is abelian.