Home
Class 12
MATHS
Let omega!=1 be cube root of unity and S...

Let `omega!=1` be cube root of unity and `S` be the set of all non-singular matrices of the form `[(1,a, b), (omega, 1, c), (omega^2, omega, 1)]` , where each of `a ,b` and `c` is either `omegaoromega^2` Then the number of distinct matrices in the set `S` is
a. `2`
b. `6`
c. `4`
d. `8`

A

2

B

6

C

4

D

8

Text Solution

Verified by Experts

The correct Answer is:
A
For being nonsingular,
`|(1,a,b),(omega,1,c),(omega^(2),omega,1)| ne 0`
or `ac omega^(2)-(a+c) omega+1 ne 0`
Hence, number of possible triplets of (a, b, c) is 2.
i.e., `(omega, omega^(2), omega)` and `(omega, omega, omega)`.
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise Single correct Answer|34 Videos

  • MATRICES

    CENGAGE|Exercise Multiple Correct Answer|7 Videos

  • MATRICES

    CENGAGE|Exercise JEE Main Previous Year|11 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

Let omega != 1 be cube root of unity and S be the set of all non-singular matrices of the form [(1,a,b),(omega,1,c),(omega^2,theta,1)], where each of a,b, and c is either omega or omega^2. Then the number of distinct matrices in the set S is (a) 2 (b) 6 (c) 4 (d) 8

Identify the singular and non-singular matrices: [(1,2,3),(4,5,6),(7,8,9)]

If omega is a cube root of unity and (omega-1)^7=A+Bomega then find the values of A and B

If omega is an imaginary cube root of unity, then (1+omega-omega^2)^7 is equal to (a) 128omega (b) -128omega (c) 128omega^2 (d) -128omega^2

If omega is the cube root of unity, then then value of (1 - omega) (1 - omega^(2))(1 - omega^(4))(1 - omega^(8)) is

If omega is a cube root of unity, then find the value of the following: (1+omega-omega^2)(1-omega+omega^2)

If omega is a cube root of unity, then the value of (1 - omega + omega^2)^4 + (1 + omega - omega^2)^(4) is ……….

If omega is a non real cube root of unity, then (a+b)(a+b omega)(a+b omega^2)=

If the cube roots of unity are 1, omega, omega^(2) then the roots of the equation (x-1)^(3)+8=0 , are

CENGAGE-MATRICES-JEE Advanced Previous Year
  1. The number of 3xx3 matrices A whose entries are either 0or1 and for wh...

    Text Solution

    |

  2. Let omega!=1 be cube root of unity and S be the set of all non-singula...

    Text Solution

    |

  3. Let P=[a("ij")] be a 3xx3 matrix and let Q=[b("ij")], where b("ij")=2^...

    Text Solution

    |

  4. Let P=[[1,0,0],[4,1,0],[16,4,1]]and I be the identity matrix of order ...

    Text Solution

    |

  5. How many 3xx3 matrices M with entries from {0,1,2} are there, for whic...

    Text Solution

    |

  6. Let Ma n dN be two 3xx3 non singular skew-symmetric matrices such that...

    Text Solution

    |

  7. Let omega be a complex cube root of unity with omega!=1a n dP=[p(i j)]...

    Text Solution

    |

  8. For 3xx3 matrices Ma n dN , which of the following statement (s) is (a...

    Text Solution

    |

  9. Let M be a 2xx2 symmetric matrix with integer entries. Then M is inver...

    Text Solution

    |

  10. Let m and N be two 3x3 matrices such that MN=NM. Further if M!=N^2 and...

    Text Solution

    |

  11. Let Xa n dY be two arbitrary, 3xx3 , non-zero, skew-symmetric matrices...

    Text Solution

    |

  12. Let p=[(3,-1,-2),(2,0,alpha),(3,-5,0)], where alpha in RR. Suppose Q=[...

    Text Solution

    |

  13. Which of the following is (are) NOT the square of a 3xx3 matrix with r...

    Text Solution

    |

  14. Let S be the set of all column matrices [(b(1)),(b(2)),(b(3))] such th...

    Text Solution

    |

  15. Let A be the set of all 3 xx 3 symmetric matrices all of whose entrie...

    Text Solution

    |

  16. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

    Text Solution

    |

  17. Let A be the set of all 3xx3 symmetric matrices all of whose either 0 ...

    Text Solution

    |

  18. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

    Text Solution

    |

  19. Let P be an odd prime number and T(p) be the following set of 2xx2 mat...

    Text Solution

    |

  20. Let p be an odd prime number and Tp, be the following set of 2 xx 2 ma...

    Text Solution

    |