What is the multiplicative inverse property?

Answer 1

For any two non zero integers a and b, a/b x b/a = 1

-------------------------------------

For every number a ≠ 0 there is a number denoted by a^-1 (a to the power -1) such that:

a × a^-1 = a^-1 × a = 1

Answer 2

Suppose you have a set S in which the multiplicative identity is i. Then for an element x, y is its multiplicative inverse if (and only if) x*y = i = y*x.

Multiplication need not be commutative but for the multiplicative identity it must be.