Matrices And Determinants

Let \(\omega\) \(\ne\) 1 be a cube root of unity and S be the set of all non-singular matrices of the form \(\left[ {\matrix{ 1 & a & b \cr \omega & 1 & c \cr {{\omega ^2}} & \omega & 1 \cr } } \right]\), where each of a, b, and c is either \(\omega\) or \(\omega\)². Then the number of distinct matrices in the set S is