Normal subgroup is where
left coset = right coset
Now we need to verify, option $C)$ and $D)$
Say the coset is$\begin{bmatrix} 1 &0 \\ 0 &1 \end{bmatrix}$
So, according to normal subgroup
$\begin{bmatrix} 1 &0 \\ 0 &1 \end{bmatrix}$.$\begin{bmatrix} 1 &b \\ 0 &1 \end{bmatrix}$=$\begin{bmatrix} 1 &b \\ 0 &1 \end{bmatrix}$.$\begin{bmatrix} 1 &0 \\ 0 &1 \end{bmatrix}$
which satisfies.
So, it is normal subgroup
$\begin{bmatrix} 1 &b\\ 0 &1 \end{bmatrix}$ it is also a quotient group of $\begin{bmatrix} a &b\\ 0 &a^{-1} \end{bmatrix}$
where quotient value is only 1
and quotient group and normal subgroup are isomorphic and quotient group is subset of normal subgroup
Answer will be both C) and D)