The row and column for e are obvious. Then you can fill in the rest by trial and error - a fairly systematic approach will give the answer in no time.
Let G ={e,a,b} be a set containing three distinct elements and * be an operation on G such that {G,*} is a group with identity element e.
a) Determine the operation table for *. ( Note there is only one possible solution to this problem.)
b) Is your group abelian? What can you conclude about any group of order 3?
1. Operation table
* e a b
e e a b
a a b e
b b e a
2. Just use the Abelian group definition from Abelian group - Wikipedia, the free encyclopedia