How to show that the quotient group is isomorphic to $(\mathbb R,+)$ Let 
$$G=
\begin{Bmatrix}
\begin{bmatrix} 
a & b \\
0 & a^{-1}
\end{bmatrix} \colon 
a,b\in \mathbb R; a>0
\end{Bmatrix} 
\mbox{ and } 
N=
\begin{Bmatrix}
\begin{bmatrix} 
1 & b 
\\ 0 & 1 
\end{bmatrix} 
\colon b\in \mathbb{R}
\end{Bmatrix}
$$
Prove that $G/N$ is isomorphic to $(\mathbb R,+)$ and $G/N$ is isomorphic to $(\mathbb R^{+},*)$.
I have to get a onto homomorphism from $G$ to $\mathbb R$ whose kernel is $N$ .I am failing to do so.
Any hint would suffice.

Consider the natural map: $G\rightarrow G$, given by 
$$
\begin{bmatrix} 
a & b \\
0 & a^{-1}
\end{bmatrix}
\mapsto 
\begin{bmatrix} 
a & 0 
\\ 0 & a^{-1} 
\end{bmatrix}. 
$$
Is it a homomorphism? What is kernel and image?
