Question

What is the inverse of an if (Z,*) is a group with a*b = a+b+1 ∀ a, b ∈Z?

Answer 1

Answer:

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.