If `w` is an imaginary cube root of unity, find the value of `|[1,w, w^2],[ w ,w^2 ,1],[w^2 ,1,w]|` .

Options

A. 1
B. 0
C. `w^(2)`
D. w

Answer

B

Explanation

Applying `C_(1) rarr C_(1) + C(2) + C_(3)`, we have
`Delta = |(1 + w + w^(2),w,w^(2)),(w + w^(2) + 1,w^(2),1),(w^(2) + 1 + w,1,w)|`
`rArr Delta = |(0,w,w^(2)),(0,w^(2),1),(0,1,w)| " "[ :' 1 + w + w^(2) = 0]`
`rArr Delta = 0` [ `:' C_(1)` consists of all zeros]