AMC 10B 2006 Problem 18

Let a_{1}, a_{2}, \ldots be a sequence for which

a_{1}=2, \quad a_{2}=3, \quad \text { and } \quad a_{n}=\dfrac{a_{n-1}}{a_{n-2}} \text { for each positive integer } n \geq 3

What is a_{2006} ?

Answer Choices
A. \dfrac{1}{2}
B. \dfrac{2}{3}
C. \dfrac{3}{2}
D. 2
E. 3