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ring is commutative, either x^2=1 or x^n=0

Source: VJIMC 2012 2.3

May 31, 2021
Ring Theoryabstract algebragroup theory

Problem Statement

Let (A,+,⋅)(A,+,\cdot) be a ring with unity, having the following property: for all x∈Ax\in A either x2=1x^2=1 or xn=0x^n=0 for some n∈Nn\in\mathbb N. Show that AA is a commutative ring.
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