Question

If (G*) is group, than show that (a-¹)-¹=a​

Answer 1

Step-by-step explanation:

Don't know sry can't help

Answer 2

Answer:

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Step-by-step explanation:

Note that by definition (a−1)−1(a−1)−1 and aa are both inverse elements of a−1a−1. Since in a group each element has a unique inverse, we can conclude that (a−1)−1=a(a−1)−1=a.

I will now prove that in a group inverse elements are unique.

Suppose b,c∈Gb,c∈G such that ba=e=abba=e=ab and ca=e=acca=e=ac That is to say, bb and cc are both inverse elements of aa where ee is the identity of the group GG.

Then we have b=be=b(ac)=(ba)c=ec=cb=be=b(ac)=(ba)c=ec=c

Therefore b=cb=c and inverse elements are uniqu