Number of elements in a ring with identity.

[Stephen88]

Homework Statement

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?

Homework Equations

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 .

 

[sunjin09]

never mind