A $2 \times 2$ matrix $A$ such that $A^n$ is the identity matrix So basically determine a $2 \times 2$ matrix $A$ such that $A^n$ is an identity matrix, but none of $A^1, A^2,..., A^{n-1}$ are the identity matrix. (Hint: Think geometric mappings) 
I don't understand this question at all, can someone help please?

Hint: Rotate through $\frac{2\pi}{n}$. 
