Let $$X(e^{j \omega}) = \sum_{n = -\infty}^{\infty} x[n] e^{-j \omega n}$$ and $$x[n] = \frac{1}{2 \pi} \int_{-\pi}^{\pi}X(e^{j \omega})e^{j \omega n}d \omega$$. If $$X(e^{j \omega}) = \frac{1}{(1 - 0.2e^{-j \omega})(1 - 0.1e^{-j \omega})}$$, what is x[n] in terms of unit discrete step function u(n)?

A

$$2(0.2)^n u(n) - (0.1)^n u(n)$$

B

$$2(0.1)^n u(n) - (0.2)^n u(n)$$

C

$$(0.2)^n u(n) - (0.1)^n u(n)$$

D

$$(0.1)^n u(n) - (0.2)^n u(n)$$