$G=(\mathbb{R}^*,\cdot)$ , $N=\{-1,1\}$. prove that $G/N\cong (\mathbb{R}_+,\cdot)$ Let $G=(\mathbb{R}^*,\cdot)$ and $N=\{-1,1\}$. I need to prove that $G/N\cong (\mathbb{R}_+,\cdot)$
This is all the details that I have in the exercise, usually given  $\varphi$ such that $\varphi$ is a homomorphism, but here how colud I prove the isomorphism? 

The absolute value is a map from the non-zero reals to the positive reals that  conveniently is also a homomorphism with respect to multiplication. 
Some further details need to be checked, which I do not spell out. 
