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 det (A) is not 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 ENGLISH|Exercise Matrix Type|5 Videos

  • MATRICES

    CENGAGE ENGLISH|Exercise Numerical Value Type|27 Videos

  • MATRICES

    CENGAGE ENGLISH|Exercise Multiple Correct Answer|49 Videos

  • MATHMETICAL REASONING

    CENGAGE ENGLISH|Exercise Archives|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Single Correct Answer Type|46 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 P be the relation defined on the set of all real number such that P = [(a, b) : sec^2 a-tan^2 b = 1] . Then P is:

If p_1a n dp_2 are two odd prime numbers such that p_1> p_2, then p1 2-p2 2 is an even number (b) an odd number an odd prime number (c) a prime number

Let z be a complex number satisfying equation z^p-z^(-q)=0,\ where\ p ,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

If p and q are co-prime numbers, then p^2 and q^2 are (a) coprime (b) not coprime (c) even (d) odd

Let {t_(n)} is an A.P If t_(1) = 20 , t_(p) = q , t_(q) = p , find the value of m such that sum of the first m terms of the A.P is zero .

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

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

If a, b, c are distinct real numbers such that a, b, c are in A.P. and a^2, b^2, c^2 are in H. P , then

If a ,b ,c are in A.P., the a/(b c),1/c ,1/b will be in a. A.P b. G.P. c. H.P. d. none of these

CENGAGE ENGLISH-MATRICES-Linked Comprehension Type
  1. Let A=[a("ij")] be 3xx3 matrix and B=[b("ij")] be 3xx3 matrix such tha...

    Text Solution

    |

  2. Let A=[(1,0,0),(1,0,1),(0,1,0)] satisfies A^(n)=A^(n-2)+A^(2)-I for n ...

    Text Solution

    |

  3. Let A=[(1,0,0),(1,0,1),(0,1,0)] satisfies A^(n)=A^(n-2)+A^(2)-I for n ...

    Text Solution

    |

  4. Let A=[(1,0,0),(1,0,1),(0,1,0)] satisfies A^(n)=A^(n-2)+A^(2)-I for n ...

    Text Solution

    |

  5. Let for A=[(1,0,0),(2,1,0),(3,2,1)], there be three row matrices R(1),...

    Text Solution

    |

  6. Let for A=[(1,0,0),(2,1,0),(3,2,1)], there be three row matrices R(1),...

    Text Solution

    |

  7. A and B are square matrices such that det. (A)=1, B B^(T)=I, det (B) g...

    Text Solution

    |

  8. A and B are square matrices such that det. (A)=1, B B^(T)=I, det (B) g...

    Text Solution

    |

  9. Let A be an mxxn matrix. If there exists a matrix L of type nxxm such ...

    Text Solution

    |

  10. Let A be an mxxn matrix. If there exists a matrix L of type nxxm such ...

    Text Solution

    |

  11. Let A be an mxxn matrix. If there exists a matrix L of type nxxm such ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |