Let $$G = \left\{\left(\begin{array}{cc}a & b \\ 0 & a^{-1}\end{array}\right) : a, b \in \mathbb{R}, a > 0\right\}, \quad N = \left\{\left(\begin{array}{cc}1 & b \\ 0 & 1\end{array}\right) : b \in \mathbb{R}\right\}.$$ Which of the following are true? (A) $G/N$ is isomorphic to $\mathbb{R}$ under addition. (B) $G/N$ is isomorphic to $\{a \in \mathbb{R} : a > 0\}$ under multiplication. (C) There is a proper normal subgroup $N'$ of $G$ which properly contains $N$. (D) $N$ is isomorphic to $\mathbb{R}$ under addition.
Let
$$G = \left\{\left(\begin{array}{cc}a & b \\ 0 & a^{-1}\end{array}\right) : a, b \in \mathbb{R}, a > 0\right\}, \quad N = \left\{\left(\begin{array}{cc}1 & b \\ 0 & 1\end{array}\right) : b \in \mathbb{R}\right\}.$$
Which of the following are true?\\
(A) $G/N$ is isomorphic to $\mathbb{R}$ under addition.\\
(B) $G/N$ is isomorphic to $\{a \in \mathbb{R} : a > 0\}$ under multiplication.\\
(C) There is a proper normal subgroup $N'$ of $G$ which properly contains $N$.\\
(D) $N$ is isomorphic to $\mathbb{R}$ under addition.