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. `A^2=A` b. `A^2=I` c. `A B=O` d. `B A=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 B=Aa n dB A=B , then a. A^2B=A^2 b. B^2A=B^2 c. A B A=A d. B A B=B

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

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, b],[ c,1-a]] is an idempotent matrix and f(x)=x-x^2 , bc=1/4 , then the value of 1//f(a) is ______.

A square matrix A is used to be an idempotent matrix if A^(2) = A . If A is an idempotent matrix and B = I -A, then-

A square matrix A is used to be an idempotent matrix if A^(2) = A . If A, B and A + B are idempotent matrices, then-

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

If 2b+(a-b)i=2+3i, then find a and b. .

If A^2-A+I=0, then the inverse of A is a. A^(-2) b. A+I c. I-A d. A-I

If A is a nilpotent matrix of index 2, then for any positive integer n ,A(I+A)^n is equal to (a) A^(-1) (b) A (c) A^n (d) I_n

CENGAGE PUBLICATION-MATRICES-All Questions
  1. Let M be a 2xx2 symmetric matrix with integer entries. Then M is inver...

    Text Solution

    |

  2. For 3xx3 matrices M \ a n d \ N , which of the following statement (s)...

    Text Solution

    |

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

    Text Solution

    |

  4. If A^(-1)=[[1,-1, 2],[0, 3,1],[ 0 ,0,-1/3]] , then |A|=-1 b. adj A=[[-...

    Text Solution

    |

  5. If [(1,0,0),(0,1,0),(0,0,1)][(x),(y),(z)]=[(1),(-1),(0)] , find x ,\ y...

    Text Solution

    |

  6. Which of the following statements is/are true about square matrix A or...

    Text Solution

    |

  7. If A is an invertible matrix, then (a d jdotA^(-1)) is equal to a.[a ...

    Text Solution

    |

  8. If A=(a(i j))(nxxn) and f is a function, we define f(A)=((f(a(i j))))(...

    Text Solution

    |

  9. Suppose a1, a2, are real numbers, with a1!=0. If a1, a2,a3, are in A...

    Text Solution

    |

  10. If A,B,C are three square matrices of the same order, then A B=A C =>...

    Text Solution

    |

  11. Let A=[1 0 1 1] . Then which of following is not true? (lim)(nvecoo)1/...

    Text Solution

    |

  12. If alpha,beta,gamma are real numbers, then without expanding at any...

    Text Solution

    |

  13. The matrix A=[(-5,-8,0),(3,5,0),(1,2,-1)] is (A) idempotent mat...

    Text Solution

    |

  14. If P (E) = 0.05, what is the probability of ‘not E’?

    Text Solution

    |

  15. If A=[[a,b],[c,d]] (where b c!=0 ) satisfies the equations x^2+k=0,t h...

    Text Solution

    |

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

    Text Solution

    |

  17. Given the matrix A=[[x,3,2],[1,y,4],[2,2,z]]. If xyz=60 and 8x+4y+3z=2...

    Text Solution

    |

  18. Let A +2B=[[1, 2, 0],[ 6,-3, 3],[-5, 3, 1] ] and 2A-B=[[2,-1, 5 ],[2,-...

    Text Solution

    |

  19. Which of the following in an orthogonal matrix

    Text Solution

    |

  20. If k in Ro then det{adj(k In)} is equal to (A) K^(n-1) (B) K^((n-1)...

    Text Solution

    |