I know this should be really easy, but I can't seem to figure it out. I don't really want an out an out answer if possible, just a starting point to work from.

The question reads as follows:

"Let R be an integral domain, and suppose satisfies . Prove that we must either have x = 1 or x = -1."

I started off by saying that if we have:

Then x has an inverse, where .

This means that x is also in the group of units of R, but then I just don't know where to go... part of me wants to ignore the commutative law and say something like:

So by right multiplication then x = 1 and . But that just seems off.

Thanks for any help.

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Dave