Home
Class 12
MATHS
If B is an idempotent matrix, and A=I-B ...

If `B` is an idempotent matrix, and `A=I-B ,` then `A^2=A` b. `A^2=I` c. `A B=O` d. `B A=O`

A

`A^(2) = A`

B

`A^(2) = I`

C

`AB=O`

D

`BA= O`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
`because A = I - B`
`rArr A^(2) =I^(2) + B^(2) - 2 B= I - B = A ` [ `because` B is idempotent ]
and `AB= B- B^(2) = B - B= 0 ` [ nill matrix]
and `BA = B- B^(2) = B - B = 0 ` [ null matrix]
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|16 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|10 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|30 Videos

  • MATHEMATICAL INDUCTION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|31 Videos

Similar Questions

Explore conceptually related problems

" 1.If "B" is an idempotent matrix and "A=I-B" then "AB=

If B is an idempotent matrix,and A=I-B then a.A^(2)=A b.A^(2)=I c.AB=O d.BA=O

If A is an idempotent matrix, then show that B=l-A is also idempotent and AB=BA=0

If A,B,A+I,A+B are idempotent matrices,then AB is equal to BA b.-BA c.I d.O

If for the matrix A ,\ A^3=I , then A^(-1)= A^2 (b) A^3 (c) A (d) none of these

A square matix A is called idempotent if (A) A^2=0 (B) A^2=I (C) A^2=A (D) 2A=I

If Z is an idempotent matrix,then (I+Z)^(n)I+2^(n)Z b.I+(2^(n)-1)Z c.I-(2^(n)-1)Zd . none of these

If A is non-diagonal involuntary matrix,then A=I=O b.A+I=O c.A=I is nonzero singular d.none of these

If the matrix AB is zero,then It is not necessary that either A=O or,B=O (b) A=O or B=O( c) A=O and B=0 (d) all the above statements are wrong