Matrices And Determinants

Let \(z = {{ - 1 + \sqrt 3 i} \over 2}\), where \(i = \sqrt { - 1}\), and r, s \(\in\) {1, 2, 3}. Let \(P = \left[ {\matrix{ {{{( - z)}^r}} & {{z^{2s}}} \cr {{z^{2s}}} & {{z^r}} \cr } } \right]\) and I be the identity matrix of order 2. Then the total number of ordered pairs (r, s) for which P² = \(-\)I is ____________.