Let ω be a complex cube root of unity with ω ≠ 1 and P = p ij be a n x n matrix with p ij = ω i + j . Then P 2 ≠ 0 , when n =

Step-by-step solution

n = 1 n = 2 P = ω 2 P = ω 2 ω 3 ω 3 ω 4 = ω 2 1 1 ω P 2 = ω 4 ≠ 0 P 2 = ω 4 + 1 ....... ....... ....... ≠ 0 n = 3 P = ω 2 1 ω 1 ω ω 2 ω ω 2 1 ω 2 1 ω 1 ω ω 2 ω ω 2 1 = 0 0 0 0 0 0 0 0 0 Similarly P 2 ≠ 0 when n is not multiple of 3.