- #1
playa007
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Homework Statement
Let R be a ring that satisfies a^2 = a for all a in R. Prove that R is a commutative ring
Homework Equations
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