In an integral domain, there are at most two square roots of 1

Prove that if R is an integral domain and x^2 = 1 for some x \in R, then x = 1 or x = -1.


If x^2 = 1, then x^2 - 1 = 0. Evidently, then, (x-1)(x+1) = 0. Since R is an integral domain, we must have x-1 = 0 or x+1 = 0; thus x = 1 or x = -1.

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