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If a1, a2, . . . , an belong to a group, what is the

Chapter 2, Problem 28E

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QUESTION:

If a1, a2, . . . , an belong to a group, what is the inverse of a1a2 . . . an?

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QUESTION:

If a1, a2, . . . , an belong to a group, what is the inverse of a1a2 . . . an?

ANSWER:

Step 1 of 3

To find the inverse of  :

Consider  is a group.

Let 

By the properties of a group, we have:

In view of this property, using method of induction to prove:

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