Let $$z = \frac{-1 + \sqrt{3}i}{2}$$, where $$i = \sqrt{-1}$$, and $$r, s \in \left\{1, 2, 3\right\}$$. Let $$P = \begin{bmatrix}(-z)^r & z^{2s} \\z^{2s} & z^r \end{bmatrix}$$ and I be the identity matrix of order 2. Then the total number of ordered pairs $$(r, s)$$ for which $$P^2 = -I$$ is