# Q1-(Uniqueness of the inverse:). Show that for every a ∈ G, the inverse of a is unique. We will denote the inverse of a by a−1. Also prove the following:  (b · a)−1 = a−1 · b−1 for all a, b ∈ G.

Question

Q1-(Uniqueness of the inverse:). Show that for every a ∈ G, the inverse of a is unique. We will denote the inverse of a by a−1. Also prove the following:

(b · a)−1 = a−1 · b−1 for all a, b ∈ G.