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.
under component wise addition.

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.
under component wise addition.