Let $$\omega$$ be a complex cuberoot of unity with $$\omega \neq 1$$ and $$P = [p_{ij}]$$ be a $$n \times n$$ matrix with $$p_{ij} = \omega^{i+j}$$. Then $$P^2 \neq 0$$, when n =

A

57

B

55

C

58

D

56