Let A = (2, -1, -1; 1, 0, -1; 1, -1, 0) and B = A - I. If ω=(√ 3 i-1)/2, then the number of elements in the set {n ∈{1,2, …, 100}: A^n+(ω B)^n=A+B}…

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