Primitive Roots and Order

Question

Determine ord$_{17}2^{12}$.

Below is what I think the answer is. Any comments and suggestions on how to approach the problem would be great!

So does this mean that:

Since,

$ 2^{12} \equiv (2^6)^2\equiv (13)^2\equiv 169 \equiv 16$ (mod $17$).

Hence, ord$_{17}2^{12} = 16 $

Answer 1

Since $2^{12}\equiv16\equiv-1\pmod{17}$, $(2^{12})^2\equiv1\pmod{17}$ and therefore $\operatorname{ord}_{17}2^{12}=2$.