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Prove: If G is a group, a E G, and a * b = b for some bEG, then a is the identity

Chapter 5, Problem 5.22

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QUESTION:

Prove: If G is a group, a E G, and a * b = b for some bEG, then a is the identity elementofG.

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QUESTION:

Prove: If G is a group, a E G, and a * b = b for some bEG, then a is the identity elementofG.

ANSWER:

Step 1 of 2

 And G is a group

And for some

Some G is a group so the inverse of every element of every element exists.

So let be the inverse of b

Since G is a group, an identity element exists.

Let,be the identity element

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