Thread: Need some help with groups..

I can see that it is true, but not sure how to prove it...

Problem:

Let G be a group of order 3, and let, e,a,b, be the three elements of G, where e is the identity of the group. SHOW that b must be the inverse of a.

TIA

Originally Posted by ginafara

I can see that it is true, but not sure how to prove it...

Problem:

Let G be a group of order 3, and let, e,a,b, be the three elements of G, where e is the identity of the group. SHOW that b must be the inverse of a.

TIA

G is closed and each of its elements are distinct so is equal to e, a, or b. Well and , so we are left with . (Similarly for .)

-Dan