Integral Domain: Solving a^2=1 with at Most 2 Solutions

[Rederick]

Homework Statement

Let R be an integral domain with identity element 1. Show that there at most two elements "a" in R such that a^2=1

Homework Equations

The Attempt at a Solution

Being an integral domain implies that if ab=0, then a=0 or b=0. a^2=1 implies a=1. Then (a)(a) = (1)(1). This seems like a simple problem but I'm not sure how to properly state that there are "at most 2 elements."

 

[micromass]

Saying that a²=1, is thesame as saying that a²-1=0. Maybe you can factorize the left hand side...

 

[Rederick]

Thank you. Got it