GROUPS 4

Theorem 3 ( The uniqueness of identity & inverse elements in G )

In a group G with binary operation *, there is only one element e in G such that

e*x = x*e = x

for all x in G.

Likewise, for each a in G, there is only one element a' in G that

a'*a = a*a' = e

In summary, the identity & inverse of each element are unique in a group.