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The determinant of the matrix A=|(1,1,1)...

The determinant of the matrix `A=|(1,1,1),(1,omega,omega^2),(1,omega^2,omega)|,` where `omega=e(2pii)/3,` is

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Let omega=-1/2+i(sqrt(3))/2 . Then the value of the determinant |(1,1,1),(1,-1-omega^2,omega^2),(1,omega^2,omega^4)| is (A) 3omega (B) 3omega(omega-1) (C) 3omega^2 (D) 3omega(1-omega)

Prove that the value of determinant |{:(1,,omega,,omega^(2)),(omega ,,omega^(2),,1),( omega^(2),, 1,,omega):}|=0 where omega is complex cube root of unity .

The value of the determinant |(1,omega^(3),omega^(5)),(omega^(3),1,omega^(4)),(omega^(5),omega^(4),1)| , where omega is an imaginary cube root of unity, is

If omega is a complex cube root of unity, then a root of the equation |(x +1,omega,omega^(2)),(omega,x + omega^(2),1),(omega^(2),1,x + omega)| = 0 , is

Let omega=-1/2+i(sqrt(3))/2, then value of the determinant [[1, 1, 1],[ 1,-1-omega^2,-omega^2],[1, omega^2,omega^4]] is (a) 3omega (b) 3omega(omega-1) (c) 3omega^2 (d) 3omega(1-omega)

Evaluate |(1,omega,omega^2),(omega,omega^2,1),(omega^2,omega, omega)| where omega is cube root of unity.

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

Let omega be a complex number such that 2omega+1=z where z=sqrt(-3) . If |{:(1,1,1),(1,-omega^(2)-1,omega^(2)),(1,omega^(2),omega^(7))|=3k , then k is equal to

If 1.omega, omega^2 are the roots of unity, then Delta=|(1,omega^n,omega^(2n)),(omega^n,omega^(2n),1),(omega^(2n),1,omega^n)| is equal to

If omega is an imaginary cube root of unity, then the value of the determinant |(1+omega,omega^2,-omega),(1+omega^2,omega,-omega^2),(omega+omega^2,omega,-omega^2)|

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