Question

What is the ivnerse of a if (Z, *) is a group with a*b=a+b+1 for a, b in Z​

Answer 1

Answer:

b is the inverse of a if and only if a*b = b*a = identity. Note that for this group, identity = -1 since a*(-1) = a - 1 + 1 = a ∀a ∈ Z. Fix a ∈ Z