Home
Class 12
MATHS
Let P be an odd prime number and T(p) be...

Let P be an odd prime number and `T_(p)` be the following set of `2xx2` matrices :
`T_(P)={A=[(a,b),(c,a)]: a, b, c in {0, 1, ... , p-1}}`
The number of A in `T_(p)` such that A is either symmetric or skew-symmetric or both, and det (A) divisible by p, is

A

`(p-1) (p^(2)-p+1)`

B

`p^(3)-(p-1)^(2)`

C

`(p-1)^(2)`

D

`(p-1) (p^(2)-2)`

Text Solution

Verified by Experts

The correct Answer is:
C
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 p be an odd prime number and T_p , be the following set of 2 xx 2 matrices T_p={A=[(a,b),(c,a)]:a,b,c in {0,1,2,.........p-1}} The number of A in T_p , such that A is either symmetric or skew-symmetric or both, and det (A) divisible by p is

Let A and B be two square matrices of the same size such that AB^(T)+BA^(T)=O . If A is a skew-symmetric matrix then BA is

Let Aa n dB be two nonsinular square matrices, A^T a n dB^T are the transpose matrices of Aa n dB , respectively, then which of the following are correct? B^T A B is symmetric matrix if A is symmetric B^T A B is symmetric matrix if B is symmetric B^T A B is skew-symmetric matrix for every matrix A B^T A B is skew-symmetric matrix if A is skew-symmetric

If [{:(0,p,3),(2,q^2 , -1),(r, 1,0):}] is skew-symmetric , find the values of p , q and r

Let z be a complex number satisfying equation z^p=z^(-q),w h e r ep ,q in N ,t h e n (A) if p=q , then number of solutions of equation will be infinite. (B) if p=q , then number of solutions of equation will be finite. (C) if p!=q , then number of solutions of equation will be p+q+1. (D) if p!=q , then number of solutions of equation will be p+qdot

lf r, s, t are prime numbers and p, q are the positive integers such that their LCM of p,q is r^2 t^4 s^2, then the numbers of ordered pair of (p, q) is (A) 252 (B) 254 (C) 225 (D) 224

suppose the number of elements in set A is P , the number of elements in set B is q and the number of elements in A xx B is 7 . Then p^2 +q^2 =

CENGAGE-MATRICES-JEE Advanced Previous Year
  1. Let omega be a complex cube root of unity with omega!=1a n dP=[p(i j)]...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7...

    Text Solution

    |

  16. Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7...

    Text Solution

    |

  17. Let a,b, and c be three real numbers satistying [a,b,c][(1,9,7),(8,2,7...

    Text Solution

    |

  18. Let K be a positive real number and A=[2k-1 2sqrt(k)2sqrt(k)2sqrt(k)1-...

    Text Solution

    |

  19. Let M be a 3xx3 matrix satisfying M[0 1 0]=M[1-1 0]=[1 1-1],a n dM[1 1...

    Text Solution

    |

  20. let z= (-1+sqrt(3i))/2, where i=sqrt(-1) and r,s epsilon P1,2,3}. Let ...

    Text Solution

    |