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Prove that (a + b)2 = a2 + 2ab + b2 for all a, b in a ring R iff R is commutative

Chapter 24, Problem 24.17

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QUESTION:

Prove that (a + b)2 = a2 + 2ab + b2 for all a, b in a ring R iff R is commutative.

Questions & Answers

QUESTION:

Prove that (a + b)2 = a2 + 2ab + b2 for all a, b in a ring R iff R is commutative.

ANSWER:

Step 1 of 2

Consider the expression,

                 

Solve the above equation as,

                 

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