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Prove that in a group, (a–1)–1 = a for all a.

Chapter 2, Problem 26E

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QUESTION:

Prove that in a group, \((a^{-1})^{-1} = a\) for all a.

Questions & Answers

QUESTION:

Prove that in a group, \((a^{-1})^{-1} = a\) for all a.

ANSWER:

Step 1 of 2

To prove:

In a group, for all

By the definition of group, we know that there exists an identity element  such that

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