The map ∅: Z → Z defined by ∅(n) = n + 1 for n ∈ Z is one to one and onto Z. Give the definition of a binary operation * on Z such that ∅ is an isomorphism mapping
a. (Z, +) onto (Z, *),

b. (Z, *) onto (Z, +).

In each case, give the identity element for * on Z.