Let $$\omega \neq 1$$ be a cube root of unity and S bethe set of all non-singular matrices of the form
$$\begin{bmatrix}1 & a & b\\\omega & 1 & c\\\omega^2 & \omega & 1\end{bmatrix}$$,
where each of a, b, and c is either $$\omega$$ or $$\omega^2$$. Then the number of distinct matrices in the set S is

A

2

B

6

C

4

D

8