Home
Class 12
MATHS
Let p be an odd prime number and Tp be t...

Let p be an odd prime number and `T_p` be the following set of 2 x 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) is divisible by p is: [Note: the trace of a matrix is the sum of its diagonal entries.]

A

`(p-1)^(2)`

B

`2(p-1)`

C

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

D

`2p-1`

Text Solution

Verified by Experts

The correct Answer is:
D
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MATRICES

    ML KHANNA|Exercise SELF ASSESSMENT TEST|13 Videos

  • MATHEMATICAL REASONING

    ML KHANNA|Exercise PROBLEM SET (2) ASSERTION/REASON|3 Videos

  • MAXIMA AND MINIMA

    ML KHANNA|Exercise MISCELANEOUS EXERCISE (COMPREHENSION)|3 Videos

Similar Questions

Explore conceptually related problems

Let p be an odd prime number and T_p be the following set of 2 x 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 det(A) is not divisible by p, is :

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{0,1,2,…….,p-1}} The number of A in T_(p) such that det (A) is not divisible by p is

Knowledge Check

  • Let p be prime number such that 3 < p < 50 , then p^2 - 1 is :

    A
    always divisible by 8
    B
    always divisible by 24
    C
    always divisible by 12
    D
    all of a,b,c

  • Let P be the set of prime numbers and S = { t : 2^t-1 is a prime}. Then,

    A
    `S sub P`
    B
    `P sub S`
    C
    S = P
    D
    None of these

  • If A is symmetric and B skew- symmetric matrix and A + B is non-singular and C= (A+B) ^(-1) (A-B) C^(T) AC equals to

    A
    `A + B`
    B
    `A-B`
    C
    A
    D
    B

    • Similar Questions

    Explore conceptually related problems

    Let p be an odd prime number and T_p be the following set of 2 x 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 the trace of A is not divisible by p but det(A) is divisible by p is :

    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{0,1,2,…….,p-1}} The number of A in T_(p) such that the trace of A is not divisible by p but det (A) is divisible by p is

    Let p be a prime number such that 3

    235412P+, where P is a s where P is a symmetric and Q is a skew-symmetric then Q=

    Matrices of order 33 are formed by using the elements of the set A={-3,-2,-1,0,1,2,3} then probability that matrix is either symmetric or skew symmetric is

    Home
    Profile