If `omega` is a non-real cube root of unity, then `Delta = |(a_(1) + b_(1) omega,a_(1) omega^(2) + b_(1),a_(1) + b_(1) + c_(1) omega^(2)),(a_(2) + b_(2) omega,a_(2) omega^(2) + b_(2),a_(2) + b_(2) omega + c_(2) omega^(2)),(a_(3) + b_(3) omega,a_(3) omega^(2) + b_(3),a_(3) + b_(3) omega + c_(3) omega^(2))|` is equal to

Options

A. `-1`
B. 0
C. `-omega^(2)`
D. none of these

Answer

B

Explanation

Applying `C_(2) rarr C_(2) (omega)`, we get
`Delta = (1)/(omega) |(a_(1) + b_(1) omega,a_(1) + b_(1) omega,a_(1) + b_(1) omega + c_(1) omega^(2)),(a_(2) + b_(2) omega,a_(2) + b_(2) omega,a_(2) + b_(2) omega + c_(2) omega^(2)),(a_(3) + b_(3) omega,a_(3) + b_(3) omega,a_(3) + b_(3) omega + c_(3) omega^(2))|`
`rArr Delta = (1)/(omega) xx 0 = 0 " " [ :' C_(1) and C_(2) " are indentical"]`