Isomorphism of quotient group

Question

Let $G=\left\{\begin{bmatrix}a&b\\0&a^{-1}\end{bmatrix}:a,b\in \mathbb{R}, a>0\right\}$ and $N=\left\{\begin{bmatrix}1&b\\0&1\end{bmatrix}:b\in \mathbb{R}\right\}$

Which of the following are true?

1. $G/N$ is isomorphic to $\mathbb{R}$ under Addition

2. $G/N$ is isomorphic to $\{a\in \mathbb{R}:a>0\}$ under Multiplication

3. There is a proper normal subgroup $N'$ of $G$ which properly contains $N$

4. $N$ is isomorphic to $\mathbb{R}$ under addition.

Consider $\eta:G\rightarrow N$ with $\begin{bmatrix}a&b\\0&a^{-1}\end{bmatrix}\mapsto a$ this is clealy a homomorphism with kernel $N$ so second option is correct..

Consider $\eta:G\rightarrow N$ with $\begin{bmatrix}a&b\\0&a^{-1}\end{bmatrix}\mapsto b$ this is clealy a homomorphism which is bijective so fourth option is correct..

I am not able to decide whether other options are true or false..