Determine whether the binary operation * gives a group structure on the given set. If no group results, give the first axiom in the order G1, G2, G3 that does not hold .  1) Let * be defined on Z by letting a * b =ab

Determine whether the binary operation * gives a group structure on the given set. If no group results, give the first axiom in the order G_1, G_2, G₃ that does not hold . 

1) Let * be defined on Z by letting a * b =ab

2) Let * be defined on 2Z = {2n|n ∈ Z by letting a * b = a + b 

3) Let * be defined on R⁺ by letting a * b = sqrt(ab)

4) Let * be defined on the set R^* of nonzero real numbers by letting a * b = a/b