Thread: Need some help with groups..

1. 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

2. 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 $ab$ is equal to e, a, or b. Well $ab = a \implies b = e$ and $ab = b \implies a = e$, so we are left with $ab = e \implies a^{-1} = b$. (Similarly for $ba$.)

-Dan