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Prove that A x B is Abelian iff both A and B are Abelian

Chapter 15, Problem 15.18

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QUESTION:

Prove that A x B is Abelian iff both A and B are Abelian.

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QUESTION:

Prove that A x B is Abelian iff both A and B are Abelian.

ANSWER:

Step 1 of 2

The objective is to prove that  is Abelian iff both A and B are Abelian

First suppose that A and B are abelian

For (a,b) and (x,y) in  

         

Hence,  is Abelian.

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