The operation $$\bigodot$$ is defined for all nonzero numbers a and b by $$a \bigodot b =\frac a b-\frac b a$$. If x and y are nonzero numbers, which of the following statements must be true?
I.$$x \bigodot xy = x(1 \bigodot y)$$
II.$$x \bigodot y = -(y \bigodot x)$$
III.$$\frac1 x \bigodot \frac1 y$$ =$$ y \bigodot x$$