Let A= (0, 1, 0; 0, 0, 1; 1, 0, 0) and B= (1, 1, 1; 1, 1, 1; 1, 1, 1). Then the set { n ∈ N ∣ A^n + A^n +1 + A^n +2 = B } is

Let $\displaystyle A=\left(\begin{array}{lll}0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0\end{array}\right)$ and $\displaystyle B=\left(\begin{array}{lll}1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\end{array}\right)$. Then the set $\displaystyle \left\{\mathrm{n} \in \mathbb{N} \mid \mathrm{A}^{\mathrm{n}}+\mathrm{A}^{\mathrm{n}+1}+\mathrm{A}^{\mathrm{n}+2}=\mathrm{B}\right\}$ is