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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230

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BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem
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True or False

Label each of the following statements as either true or false.

Every permutation has an inverse.

To determine

Whether the statement, ‘Every permutation has an inverse’ is true or false.

Explanation

Consider the provided statement ‘Every permutation has an inverse.’

Suppose that f is a permutation on A. Then f has left inverse as it is one-one

This means there exist left inverse g such that gf=IA, where IA is the identity.

Also f has right inverse as it is onto.

This means there exist right inverse h such that fh=IA

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