Let $\omega$ be a complex cube root of unity with $\omega \neq 1$ and $P = \left[ p _ { i j } \right]$ be a $n \times n$ matrix with $p _ { i j } = \omega ^ { i + j }$. Then $P ^ { 2 } \neq 0$, when $n =$ (A) 57 (B) 55 (C) 58 (D) 56
Let $\omega$ be a complex cube root of unity with $\omega \neq 1$ and $P = \left[ p _ { i j } \right]$ be a $n \times n$ matrix with $p _ { i j } = \omega ^ { i + j }$. Then $P ^ { 2 } \neq 0$, when $n =$
(A) 57
(B) 55
(C) 58
(D) 56