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Let z = (-1 + sqrt(3i))/(2) , where i=...

Let ` z = (-1 + sqrt(3i))/(2)` , where ` i= sqrt(-1)` , and r,s` in {1,2,3}` . Let ` P =:[((-z)^(r) ,z^(2s)),(z^(2s), z^(r))]` and I be the identity
matrix of order 2 .Then the total number of ordered pairs (r,s) for which ` p^(2) = - I ` is ______

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