If a2 + a + 1 = 0, then the value of a9 is?

Answer: Option C

$$a^2+a+1=0$$
$$\left[\begin{array}{l}{a}^3+1^3=\left(a+1\right)\left(a^2+a+1\right)\\ a^3-1^3=\left(a-1\right)\left(a^2+a+1\right)\end{array}\right]$$
$$\begin{array}{rl}& \therefore \left(a^3-1\right)=\left(a-1\right)\times 0\\ & \Rightarrow a^3-1=0\\ & \Rightarrow a^3=1\\ & \Rightarrow {\left(a^3\right)}^3=1^3\\ & \Rightarrow a^9=1\end{array}$$