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If |(a,b,0),(0,a,b),(b,0,a)| = 0, then w...

If `|(a,b,0),(0,a,b),(b,0,a)| = 0`, then which one of the following is correct ?

A

A. a/b is one of the cube roots of unity

B

B. a/b is one of the cube roots of -1

C

C. a is one of the cube roots of unity

D

D. b is one of the cube roots of unity

Text Solution

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The correct Answer is:
B
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PUNEET DOGRA-DETERMINANTS -PREV YEAR QUESTIONS
  1. The value of |(1,1,1),(1,1+x,1),(1,1,1+y)| is

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  2. Consider the following statements I. Determinant is a square matrix....

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  3. If |(a,b,0),(0,a,b),(b,0,a)| = 0, then which one of the following is c...

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  4. If a ne b ne c all are positive, then the value of determinant |(a,b,c...

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  5. If any two adjacent rows or columns of a determinant are interchanged ...

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  6. The determinant of a skew symmetric matrix of odd order is

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  7. If C(ij) is the cofactor of the element a(ij) of the determinant |{:(2...

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  8. What is the value of the determinant |(1,bc,a(b+c)),(1,ca,b(c+a)),(1,a...

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  9. If D is determinant of order 3 and D' is the determinant obtained by r...

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  10. Consider the following statements I. A matrix is not a number. II....

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  11. The roots of the equation |(1,t-1,1),(t-1,1,1),(1,1,t-1)| = 0 are

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  12. The value of the determinant |(m,n,p),(p,m,n),(n,p,m)|

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  13. If each element in a row of a determinant is multiplied by the same fa...

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  14. If two rows (or column) are identical or Proportional the value of the...

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  15. If |(8,-5,1),(5,x,1),(6,3,1)| = 2, then what is the value of x ?

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  16. If A = ((1,2),(2,3))and = ((1,0),(1,0)), then what is the value of det...

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  17. What is the value of |(-a^(2),ab,ac),(ab,-b^(2),bc),(ac,bc,-c^(2))| ?

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  18. What is the value of |(1,omega,2 omega^(2)),(2,2omega^(2),4 omega^(3))...

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  19. The root of the equation |(x,alpha,1),(beta,x,1),(beta,gamma,1)| = 0 a...

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  20. If |(p,-q,0),(0,p,q),(q,0,p)|=0, then which one of the following is co...

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