Why is commutative property not applicable in division?

Answer 1

One counterexample should be enough to disprove such an assumption. For example, 2 / 1 = 2, while 1 / 2 = 0.5. The two are not the same, ergo, the commutative property doesn't apply.Let's say that there is no statement or theorem in the sense that every operation is commutative; some are, some aren't.

By the way, you can convert any division into a multiplication - in which case it IS commutative. For example, 5 divided by 2 is the same as 5 times 1/2; the multiplication 5 times 1/2 is the same as 1/2 times 5.

Answer 2

If the commutative property were applicable then for any two numbers, X and Y,X/Y = Y/X
which would imply X^2 = Y^2 and so X = +/-Y

thus there could be only two numbers.