Solution:
Solution
∴$$\left[ \begin{matrix}1 & a & b \\\omega & 1 & c \\{{\omega }^{2}} & \omega & 1 \\\end{matrix} \right]$$, ≠ 0 (non-singular)
⇒ 1(1 - cω) - a(ω - cω2) + b(ω2 - ω2) ≠ 0
⇒ 1 - cω - aω + acω ≠ 0
⇒ (1 - cω) (1 - aω) ≠ 0
$$a\ \ne \ \cfrac{1}{\omega },\ c\ \ne \ \cfrac{1}{\omega }$$
⇒ a = ω, c = ω and b⊂ {ω, ω2}
Therefore, number of distinct solutions = 2
