Mathematics - Matrix Question with Solution | TestHub

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