`|(1,omega,-omega^2/2),(1,1,1),(1,-1,0)| = `
(a)0
(b)1
(c)`omega`
(d)`omega^2`

{[(1,omega,omega^(2)),(omega,omega^(2),1),(omega^(2),1,omega)] + [(omega,omega^(2),1),(omega^(2),1,omega),(omega,omega^(2),1)]} [(1),(omega),(omega^(2))]

If one of the cube roots of 1 be omega, then |(1,1+omega^2,omega^2),(1-i,-1,omega^2-1),(-i,-1+omega,-1)| (A) omega (B) i (C) 1 (D) 0

If omega is a complex cube root of unity then the value of determinant |[2,2 omega,-omega^(2)],[1,1,1],[1,-1,0]|= a) 0 b) 1 c) -1 d) 2

If omega is cube roots of unity, prove that {[(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega)]+[(omega,omega^2,1),(omega^2,1,omega),(omega,omega^2,1)]} [(1),(omega),(omega^2)]=[(0),(0),(0)]

If omega is a complex cube root of unity, then value of Delta=|(a_(1)+b_(1)omega, a_(1)omega^(2)+b_(1),c_(1)+b_(1)omega),(a_(2)+b_(2)omega,a_(2)omega^(2)+b_(2),c_(2)+b_(2)omega),(a_(3)+b_(3)omega,a_(3)omega^(2)+b_(3),c_(3)+b_(3)omega)| is

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

Which of the following is a non singular matrix? (A) [(1,a,b+c),(1,b,c+a),(1,c,a+b)] (B) [(1,omega, omega^2),(omega, omega^2,1),(omega^2,1,omega)] where omega is non real and omega^2=1 (C) [(1^2,2^2,3^2),(2^2,3^2,4^2),(3^2,4^2,5^2)] (D) [(0,2,-3),(-2,0,5),(3,-5,0)]

Let omega=-(1)/(2)+i(sqrt(3))/(2), then value of the determinant [[1,1,11,-1,-omega^(2)omega^(2),omega^(2),omega]] is (a) 3 omega(b)3 omega(omega-1)3 omega^(2)(d)3 omega(1-omega)