Let Rn = {(a1, a2, . . . , an) | ai [ R}. Show that the mapping Φ: (a1, a2, . . . , an) → (–a1, –a2, . . . , –an) is an automorphism of the group Rn under componentwise addition. This automorphism is called inversion. Describe the action of Φ geometrically.
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