Complex NumbersHard
Question
Let ω = - 
then value of the determinant 
is
then value of the determinant is Options
A.3ω
B.3ω (ω- 1)
C.3ω2
D.3ω(1 - ω)
Solution
Let ᐃ = 
Applying R2 → R2 - R1 ; R3 → R3 - R1
= (-2 - ω2)(ω - 1) - (ω2 - 1)2
= 2ω + 2 - ω3 + ω2 - 2(ω4 - ω2 + 1)
= 3ω2 - ω = 3ω(ω - 1) (∵ω4 = ω)
Applying R2 → R2 - R1 ; R3 → R3 - R1
= (-2 - ω2)(ω - 1) - (ω2 - 1)2
= 2ω + 2 - ω3 + ω2 - 2(ω4 - ω2 + 1)
= 3ω2 - ω = 3ω(ω - 1) (∵ω4 = ω)
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