If $A$ is an integral domain and $a^2=1$, then $a=1$ or $a=-1$

Question

I have looked at the definition of an integral domain and tried multiple equivalencies of being an integral domain but still can't figure out how to prove that:

Proposition: If $A$ is an integral domain and $a^2=1$, then $a=1$ or $a=-1$.

I would appreciate any clues on how to start this proof.

Answer 1

If $a^2=1$, then $a^2-1=0$. Factor the left hand side, and use the fact that there are no zero divisors.