Matrices And Determinants

Let $$A=\left(\begin{array}{rrr}2 & -1 & -1 \\ 1 & 0 & -1 \\ 1 & -1 & 0\end{array}\right)$$ and \(B=A-I\). If \(\omega=\frac{\sqrt{3} i-1}{2}\), then the number of elements in the \(\operatorname{set}\left\{n \in\{1,2, \ldots, 100\}: A^{n}+(\omega B)^{n}=A+B\right\}\) is equal to ____________.