1. The problem statement, all variables and given/known data 1_R=identity in the ring R. /=...not equal Having some issues with this any help will be great: Let R be a ring with identity, such that x^2 = 1_R for all 0_R /= x ,where x belongs to R. How many elements are in R? 2. Relevant equations 3. The attempt at a solution I'm looking at the element x^2 +1_R which can be = 0 or /=0. If it is the first case then x=-1 and where are done |R|=2 because of the powers of x. If the latter then (x^2 +1_R)^2=1_R...after calculation this gives x=-1/2 which is false since x^2=1 .