How to Find inverse of this: (z,*) is a group with a*b=a+b+1 then inverse of a is?

Question

How to do this? (z,*) is a group with a*b=a+b+1 then inverse of a is?

Answer 1

Identity Element = I
a*I = I*a = a
a = a + I + 1
I = -1

Inverse of a is a^-1 
a*a^-1 = I
a + a^-1 + 1 = -1
a^-1 = -( a+2 )