If ω is one of the imaginary cube roots of unity, then the value of the determinant |1 ω3 ω2 ω3 1 ω ω2 ω 1|=

Question

If ω is one of the imaginary cube roots of unity, then the value of the determinant |1 ω3 ω2 ω3 1 ω ω2 ω 1|= (A) 1 (B) 2 (C) 3 (D) none

Tardigrade Admin · Accepted Answer

Put ω3=1|1 1 ω2 1 1 ω ω2 ω 1| and open by R1 to get (1-ω2)+(1-ω)=3

Q. If $ω$ is one of the imaginary cube roots of unity, then the value of the determinant $∣ ∣ 1 ω^{3} ω^{2} ω^{3} 1 ω ω^{2} ω 1 ∣ ∣ =$