Question

Let a * b = 3a + 2b for a, b e Z. Verify that * is a
commutative binary operation on Z.
[2]​

Answer 1

It's not commutative:

a * b = 3a + 2b

but

b * a = 3b + 2a

We have equality only for

3a + 2b = 3b + 2a   →   a = b