If $$\frac{\cos \alpha}{\sin \beta} = 10$$ and $$\frac{\cos \alpha}{\cos \beta} = 11$$, then the value of $$\cos^{2} \beta$$ is:

A

$$\frac{121}{132}$$

B

$$\frac{100}{221}$$

C

$$\frac{88}{108}$$

D

$$\frac{221}{121}$$