Consider a, b ∈ Z where a * b = a + b – ab and b * a = b + a – ba

So we get a * b = b * a

**Associative:**

Consider a, b, c ∈ Z

Here,

(a * b) * c = (a + b – ab) * c = a + b – ab + c – (a + b – ab) c

We get

(a * b) * c = a + b + c – ab – bc – ca + abc

a * (b * c) = a * (b + c – bc) = a + b + c – bc – a (b + c – bc)

We get

a * (b * c) = a + b + c – an – bc – ca + abc

So (a * b) * c = a * (b * c)

**Therefore, operation on Z is associative.**