Home
Class 12
MATHS
If A is a matrix of size nxxn such that ...

If A is a matrix of size `nxxn` such that `A^(2) + A + 2I` = O then

A

A is non-singular

B

`A ne O`

C

|A| = O

D

`A^(-1) = (-1)/(2)(A + I)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

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

    CHHAYA PUBLICATION|Exercise INTEGER ANSWER TYPE|5 Videos

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

    CHHAYA PUBLICATION|Exercise MATRIX MATCH TYPE|2 Videos

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

    CHHAYA PUBLICATION|Exercise LONG ANSWER TYPE QUESTIONS|35 Videos

  • ALGEBRA

    CHHAYA PUBLICATION|Exercise JEE ADVANCED ARCHIVE 2016|5 Videos

Similar Questions

Explore conceptually related problems

If A is a matrix of order n such that A^(T)A=I and X is any matrix such that X=(A+I)^(-1) (A-I) , then show that X is skew symmetric matrix.

Let A be a matrix of order 2xx2 such that A^(2)=O . tr (A) is equal to

Knowledge Check

  • Let a be a matrix of order 2xx2 such that A^(2)=O . (I+A)^(100) =

    A
    100A
    B
    100(I+A)
    C
    100I+A
    D
    I+100A

    • Similar Questions

    Explore conceptually related problems

    Let A be an mxxn matrix. If there exists a matrix L of type nxxm such that LA=I_(n) , then L is called left inverse of A. Which of the following matrices is NOT left inverse of matrix [(1,-1),(1,1),(2,3)]?

    If A is a non-singular matrix of order nxxn such that 3ABA^(-1)+A=2A^(-1)BA , then

    Let A be a matrix of order 2xx2 such that A^(2)=O . (I+A)^(100) =

    If A is a 2xx2 matrix such that A^(2)-4A+3I=O , then prove that (A+3I)^(-1)=7/24 I-1/24 A .

    Let A be a matrix of order 3, such that A^(T)A=I . Then find the value of det. (A^(2)-I) .

    Let A be a matrix of order 2xx2 such that A^(2)=O . A^(2)-(a+d)A+(ad-bc)I is equal to

    If A is a square matrix such that A^(2)= I , then (A-I)^(3)+(A+I)^(3)-7A is equal to

    Home
    Profile