Home
Class 12
MATHS
Let I denote the 3 times 3 identity matr...

Let I denote the `3 times 3` identity matrix and P be a matrix obtained by rearranging the columns of I. Then-

A

there are six distinct choices for P and det(P)=1

B

there are six distinct choices for P and det(P) =`pm`1

C

there are some than one choices for P and some of them are not invertible.

D

there are more than one choices for P and `P^(-1)=I` in each choice.

Text Solution

Verified by Experts

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

Topper's Solved these Questions

  • ALGEBRA

    CHHAYA PUBLICATION|Exercise WBJEE ARCHIVE 2015|5 Videos
  • ALGEBRA

    CHHAYA PUBLICATION|Exercise WBJEE ARCHIVE 2016|4 Videos
  • ALGEBRA

    CHHAYA PUBLICATION|Exercise WBJEE ARCHIVE 2013|5 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

Let I denote the 3xx3 identity matrix and P be a matrix obtained by rearranging the columns of I. Then

Show that the matrix A=({:(2,-3),(3,4):}) satisfies the equation A^(2)-6A+17I=O and hence find A^(-1) where I is the identity matrix and O is the null matrix of order 2 times 2 .

Knowledge Check

  • If A is a square matrix and I is the unit matrix of the same order as A, then A.I =

    A
    A
    B
    `A^(T)`
    C
    `-A`
    D
    `A.A^(T)`
  • Let A is a 3 times 3 matrix and B is its adjoint matrix. If abs(B)=64 , then abs(A)=

    A
    `pm2`
    B
    `pm4`
    C
    `pm8`
    D
    `pm12`
  • Similar Questions

    Explore conceptually related problems

    If A^(2)-A+I=0 then the inverse of the matrix A is

    If A is an ivertible matrix of order 3xx3 and |A| = 6, then find the value of |adj.A|.

    If A is a 3×3 matrix and B is it's adjoint matrix. if |B|=64, then |A|=

    Show that the matrix A = {:[( 2,3),( 1,2) ]:} satisfies equation A^(2) -4A +I=0 where is 2xx2 identity matrix and O is 2xx2 Zero matrix. Using this equation, Find A^(-1)

    Let the metrix A be given by A = ((2,1),(3,4)) . Obtain a matrix B such that AB = BA = I where I is the unit matris of order 2. Using this matrix B, solve for x and y from the following equations: 2x + y = 15 and 3x + 4y = 23

    Let A=[a_("ij")] be 3xx3 matrix and B=[b_("ij")] be 3xx3 matrix such that b_("ij") is the sum of the elements of i^(th) row of A except a_("ij") . If det, (A)=19 , then the value of det. (B) is ________ .