Fibonacci Numbers

The Fibonacci numbers are defined by $F_0=0$, $F_1=1$, and $F_n=F_{n-1}+F_{n-2}$ for $n\ge 2$.

Implement a function to compute $F_n$. Give three solutions with different time complexities and identify each:

1. A naive recursive version.
2. An iterative version.
3. A matrix-exponentiation version.

State the time complexity of each.