(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let R be a ring that satisfies a^2 = a for all a in R. Prove that R is a commutative ring

2. Relevant equations

3. The attempt at a solution

My attempt at this solution is (ab-ba)^2 = (ba-ab)^2 is true for any ring R => (ab-ba) = (ba - ab) => 2ab = 2ba => ab = ba. The problem here is I have no method to prove that ab-ba is indeed an element of R; I'm needing help with that or a totally alternate approach to this problem is welcomed so I can perhaps gain insight

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# Homework Help: Ring theory problem

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