If the coefficient of $$x^{15}$$ in the expansion of $$\left(ax^3 + \frac{1}{bx^{\frac{1}{2}}}\right)^{15}$$ is equal to the coefficient of $$x^{-15}$$ in the expansion of $$\left(ax^{\frac{1}{3}} - \frac{1}{bx^3}\right)^{15}$$, where $$a$$ and $$b$$ are positive real numbers, then for each such ordered pair $$a, b$$:

A

$$a = b$$

B

$$ab = 1$$

C

$$a = 3b$$

D

$$ab = 3$$