question_answer

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

Answer:

(2)