Question

Please help !!

Prove that the set Z of all integers with binary operation * defined by a * b = a + b + 1, where a, b is in G is an abelian group.

Answer 1

Answer:

a∗b=a+b+1 (a,b,z is a group)

at a=−1⇒a∗b=−1+b+1=b

at b=−1⇒a∗b=a−1+1=a

⇒a∗0=a+0+1

⇒ identity element is −1.