How do I show that $\mathbb{R}-\{0\}/T$ is isomorphic to $\mathbb{R}^+$? Here, $T = \{-1, 1\}$ and  $\mathbb{R}-\{0\}$ is the multiplicative group of all the non-zero reals, and $\mathbb{R}^+$ is the multiplicative group of positive real numbers.

Hint: Can you think of a surjective homomorphism from $\mathbb{R}-\{0\}$ to $\mathbb{R}^{+}$ for which $T$ is the kernel? 
Here is a more explicit suggestion if you need it: 

 Consider the absolute value map on $\mathbb{R}-\{0\}$.

