Home
Class 12
MATHS
If A ,B ,A+I ,A+B are idempotent matrice...

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

A

`BA`

B

`-BA`

C

`I`

D

`O`

Text Solution

Verified by Experts

The correct Answer is:
B
Given `A, B, A + I, A+B` are idempotent. Hence,
`A^(2)=A, B^(2)=B, (A+I)^(2)=A+I` and `(A+B)^(2)=A+B`
`implies A^(2)+B^(2)+AB+BA=A+B`
`implies A+B+AB+BA=A+B`
`implies AB+BA=O`
Promotional Banner

Topper's Solved these Questions

  • MATHMETICAL REASONING

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

If A and B are two square matrices of the same order, then (A-B)^(2) is equal to -

If A and B are two matrices such that AB = A and BA = B then B is equal to__

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

If a ,b ,and c are in A.P., then a^3+c^3-8b^3 is equal to (a). 2a b c (b). 6a b c (c). 4a b c (d). none of these

If A and B are two square matrices such that B=-A^(-1)B A ,t h e n(A+B)^2 is equal to a. A^2+B^2 b. O c. A^2+2A B+B^2 d. A+B

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)Z d. none of these

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

A skew-symmetric matrix A satisfies the relation A^2+I=O ,w h e r e , I is a unit matrix then A is a. idempotent b. orthogonal c. of even order d. odd order

If A,B,C are three square matrices of the same order, then A B=A C => B=Cdot Then |A|!=0 b. A is invertible c. A may be orthogonal d. is symmetric

CENGAGE PUBLICATION-MATRICES-All Questions
  1. If Aa n dB are two nonzero square matrices of the same ordr such that ...

    Text Solution

    |

  2. If Aa n dB are symmetric matrices of the same order and X=A B+B Aa n d...

    Text Solution

    |

  3. If A ,B ,A+I ,A+B are idempotent matrices, then A B is equal to a.B A ...

    Text Solution

    |

  4. If A=[(0,x),(y,0)] and A^(3)+A=O then sum of possible values of xy is

    Text Solution

    |

  5. Which of the following is an orthogonal matrix ? ( ⎡ ⎢ ⎣ 6 / 7 2 / 7...

    Text Solution

    |

  6. Let A and B be two square matrices of the same size such that AB^(T)+B...

    Text Solution

    |

  7. In which of the following type of matrix inverse does not exist always...

    Text Solution

    |

  8. Let A be an nth-order square matrix and B be its adjoint, then |A B+K ...

    Text Solution

    |

  9. If A=[(a, b, c), (x, y, z), (p, q, r)], B=[(q,-b, y),(-p, a,-x),(r,-c,...

    Text Solution

    |

  10. If A(alpha,beta)=[cosalphas inalpha0-s inalphacosalpha0 0 0e^(beta)],t...

    Text Solution

    |

  11. If A=[[a+i b, c+i d],[-c+i d, a-i b]] and a^2+b^2+c^2+d^2=1,t h e n ...

    Text Solution

    |

  12. Id [(1/25, 0), (x,1/25)]=[(5, 0), (-a, 5)]^(-2) , then the value of x ...

    Text Solution

    |

  13. If A = [[1 ,2],[2,1]]and f(x)=(1+x)/(1-x), then f(A) is

    Text Solution

    |

  14. There are two possible values of A in the solution of the matrix equat...

    Text Solution

    |

  15. If A and B are two square matrices such that B=-A^(-1)B A ,t h e n(A+B...

    Text Solution

    |

  16. If A=[(1,tanx),(-tanx,1)] , show that A^T\ A^(-1)=[(cos2x,-sin2x),(sin...

    Text Solution

    |

  17. If A is order 2 square matrix such that |A|=2, then |(adj(adj(adjA)))|...

    Text Solution

    |

  18. If A=[[0, 1,2],[1,2,3],[3,a,1]]and A^(-1)[[1//2,-1//2,1//2],[-4,3,b],[...

    Text Solution

    |

  19. If nth-order square matrix A is a orthogonal, then |adj(adjA) is alway...

    Text Solution

    |

  20. Let aa n db be two real numbers such that a >1,b > 1. If A=(a0 0b) , t...

    Text Solution

    |