If $A^3=-E$ then does $A=-E$

Question

$E$ is the identity matrix. $A$ is a 2 by 2 matrix where $A^3$ is equal to $-E$. Then does $A=-E$

Answer 1

Hint: Take $A=\left[\begin{smallmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{smallmatrix}\right]$. What is $A^3$? When is it equal to $-\operatorname{Id}$?

Answer 2

Let $$A=\begin{pmatrix} \frac{1+i\sqrt3}{2}&0 \\ 0 & \frac{1-i\sqrt3}{2} \end{pmatrix}$$ from above $A\neq -E$

but if you take cube of above matrix you will get $$A^3=-E$$