Thread: Question on basic Ring theory

Hi, I'm not sure how to go about finding the solution to this question.

Let R be a ring with identity such that x² = 1_Rfor all 0_R =/= x in R. How many elements are in R?

I've just been playing around with squaring elements, like (x+1_R)² = x²+2.x+1_R =2.x+2.1_R = 1_R.

But I'm not sure where to go with this. Any help?

Maybe you should say that you find a solution on math.stackexchange.