Home
Class 11
MATHS
Which of the following is/are incorrect?...

Which of the following is/are incorrect?
(i) adjoint of a symmetric matrix is symmetric
(ii) adjoint of a unit matrix is a unit matrix
(iii) `A (adj A)=(adj A)A=absAI`
(iv) adjoint of a diagonal matrix is a diagonal matrix

A

(i)

B

(ii)

C

(iii) and (iv)

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

  • MATRICES

    OBJECTIVE RD SHARMA|Exercise Section I - Assertion Reason Type|12 Videos

  • LOGARITHMS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|21 Videos

  • MEAN VALUE THEOREMS

    OBJECTIVE RD SHARMA|Exercise Exercise|28 Videos

Similar Questions

Explore conceptually related problems

Which of the following is/are incorrect? (i).Adjoint of symmetric matrix is symmetric (ii).Adjoint of unit matrix is a unit matrix (iii). A(adjA)=(adjA)A=!|A|I (iv). Adjoint of a diagonal matrix is a diagonal matrix

Prove that adjoint of a symmetric matrix is also a symmetric matrix.

Adjoint OF square matrix

Adjoint OF a matrix || Inverse OF a matrix

Which of the following is a symmetric matrix? (A) a null matrix (B) a triangular matrix (C) an idenity matrix (D) a diagonal matrix

The diagonal elements of a skew-symmetric matrix are:

Transpose OF a matrix || Adjoint OF a matrix

determinant OF matrix || adjoint OF matrix

Find the adjoint of the given matrix and verify in each case that A.(adj A)=(adj A).A=|A\|.I. [(cos a,sin a),(sin a,cos a)]

Adjoint and Inverse of a Matrix

OBJECTIVE RD SHARMA-MATRICES-Exercise
  1. Which of the following is incorrect ?

    Text Solution

    |

  2. If A is an invertible matrix, then which of the following is correct

    Text Solution

    |

  3. Which of the following is/are incorrect? (i) adjoint of a symmetri...

    Text Solution

    |

  4. If {:[(alpha,beta),(gamma,-alpha)]:} is to be the square root of two-r...

    Text Solution

    |

  5. If for a matrix A,A^(2)+I=O where I is the indentity matrix, then A=

    Text Solution

    |

  6. If A=[a(ij)](mxxn) is a matrix of rank r then (A) rltmin{m,n} (B) rlem...

    Text Solution

    |

  7. If In is the identity matrix of order n, then rank of In is

    Text Solution

    |

  8. IfA=[a(ij)](mxxn) is a matrix of rank r and B is a square submatrix of...

    Text Solution

    |

  9. The rank of a null matrix is

    Text Solution

    |

  10. If A=[a(ij)](mxxn) is a matrix and B is a non-singular square submatri...

    Text Solution

    |

  11. Which of the following is correct ?

    Text Solution

    |

  12. If a square matrix A is orthogonal as well as symmetric, then

    Text Solution

    |

  13. Let A be a skew-symmetric of odd order, then absA is equal to

    Text Solution

    |

  14. Let A be a skew-symmetric matrix of even order, then absA

    Text Solution

    |

  15. If A is an orthogonal matrix, then

    Text Solution

    |

  16. Let A be a non-singular square matrix of order n. Then; |adjA| = |A|^(...

    Text Solution

    |

  17. Let A=[a(ij)](nxxn) be a square matrix of order 3 such that |A|=-7 an...

    Text Solution

    |

  18. If A is a non-singlular square matrix of order n, then the rank of A i...

    Text Solution

    |

  19. If A is a matrix such that there exists a square submatrix of order r ...

    Text Solution

    |

  20. Let A be a matrix of rank r. Then,

    Text Solution

    |