Question

Prove that if \(R\) is an integral domain and \(x^2=1\) for some \(x\in R\) then \(x=\pm1\).

Answer 1

Well, if \(x^2=1\), then \(x^2+(-1)=0\) which factors as \((x+1)(x+(-1))=0\)Since an integral domain has no zero divisors, either \(x+1=0\implies x=-1\) or \(x+(-1)=0\implies x=1\).

Answer 2

That works. Thanks George.

Answer 3

You're welcome.