What are the three properties of multiplication?

Answer 1

1. commutativity : ab= ba for all values of a and b.
2. distributivity: a(bc) = (ab)c for all values of a,b and c.
3. Existence of a multiplicative identity which happens to be 1 : a1 = 1a = a for all values of a.

* * * * *

Associativity is incorrectly called distributivity above: (ab)c = a(bc) and so = abc is the associative property.

Distributivity refers to two binary operations. Multiplication is distributive over addition : a(b + c) = ab + ac

Also note that there are many mathematical groups in which multiplication is not commutative: matrices being one such group.