Let G be a group. Prove that G is abelian if and only if (ab)^-1 = a^-1 * b^-1 for all a,b in G.
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Originally Posted by elninio Let G be a group. Prove that G is abelian if and only if (ab)^-1 = a^-1 * b^-1 for all a,b in G. First note we always have See why? so if G is abelian, the forward direction is clear (just move them past eachother). Conversely, if we have for all a and b in G. Just multiply on the left by (ba) and on the right by (ab)
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