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 = 1Rfor all 0R =/= x in R. How many elements are in R?
I've just been playing around with squaring elements, like (x+1R)2 = x2+2.x+1R =2.x+2.1R = 1R.
But I'm not sure where to go with this. Any help?