Home
Class 12
MATHS
If A is an 3xx3 non-singular matrix such...

If A is an `3xx3` non-singular matrix such that `A A^T=A^TA and B=A^(-1)A^T," then " B B^T` equals

A

1+B

B

I

C

`B^(-1)`

D

`(B^(-1))^(T)`

Text Solution

Verified by Experts

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

Topper's Solved these Questions

  • ALGEBRA

    CHHAYA PUBLICATION|Exercise JEE MAIN (AIEEE) ARCHIVE 2015|2 Videos

  • ALGEBRA

    CHHAYA PUBLICATION|Exercise JEE MAIN (AIEEE) ARCHIVE 2016|4 Videos

  • ALGEBRA

    CHHAYA PUBLICATION|Exercise JEE MAIN (AIEEE) ARCHIVE 2013|2 Videos

  • ADJOINT AND INVERSE OF A MATRIX AND SOLUTION OF LINEAR SIMULTANEOUS EQUATIONS BY MATRIX METHOD

    CHHAYA PUBLICATION|Exercise ASSERTION-REASON TYPE|2 Videos

  • ARCHIVE

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive|13 Videos

Similar Questions

Explore conceptually related problems

If A is an 3xx3 non-singular matrix such that A A^T=A^T A and B""=""A^(-1)A^T , then BB^T equals (1) I""+""B (2) I (3) B^(-1) (4) (B^(-1))^T

If A is a non-singular matrix such that A A^T=A^T A and B=A^(-1)A^T , the matrix B is a. involuntary b. orthogonal c. idempotent d. none of these

Knowledge Check

  • Two nxxn square matrices A and B are said to be similar if there exists a non - singular matrix C such that C^(-1) AC = B . If A and B are two singular matrices, then-

    A
    det(A) = det(B)
    B
    det(A) + det(B) = 0
    C
    det(AB) = 0
    D
    none of these

  • Two nxxn square matrices A and B are said to be similar if there exists a non - singular matrix C such that C^(-1) AC = B . If A and B are similar matrices such that det(A) = 1, then -

    A
    det(B) = 1
    B
    det(A) + det(B) = 0
    C
    det(B) = -1
    D
    none of these

    • Similar Questions

    Explore conceptually related problems

    If A and B are two non-singular matrices of order 3 such that A A^(T)=2I and A^(-1)=A^(T)-A . Adj. (2B^(-1)) , then det. (B) is equal to

    If A is non singular 3xx3 matrix and |A| =8, then |AdjA|=

    If A and B are two non-singular matrices such that A B=C ,t h e n,|B| is equal to a. (|C|)/(|A|) b. (|A|)/(|C|) c. |C| d. none of these

    If A and B are non-singular symmetric matrices such that AB=BA , then prove that A^(-1) B^(-1) is symmetric matrix.

    Let A and B be two non-singular square matrices such that B ne I and AB^(2)=BA . If A^(3)-B^(-1)A^(3)B^(n) , then value of n is

    If A is a square matrix of order less than 4 such that |A-A^(T)| ne 0 and B= adj. (A), then adj. (B^(2)A^(-1) B^(-1) A) is

    Home
    Profile