1. ## Isomorpshims

Let R^n={(a1,a2,....,an)| a_i in R}. Show that the mapping phi : (a1,a2,...,an) -> (-a1,-a2,....,-an) is an automorphism of the group R^n.

2. Originally Posted by Juancd08
Let R^n={(a1,a2,....,an)| a_i in R}. Show that the mapping phi : (a1,a2,...,an) -> (-a1,-a2,....,-an) is an automorphism of the group R^n.
You need to show $\phi: \mathbb{R}^n \to \mathbb{R}^n$ is a bijective.
And $\phi(\bold{a}+\bold{b}) = \phi(\bold{a})+\phi(\bold{b})$.