Home
Class 12
MATHS
Assertion : A matrix A is orthogonal if ...

Assertion : A matrix A is orthogonal if and only if A is non singular and `A^(-1)=A^(T)`
Reason : By definition A is orthogonal if `A A^(T)=A^(T)A=I`

A

Assertion can be proved using Reason

B

Assertion and Reason are true only for second order matrices.

C

Reason can be proved using Assertion

D

Both Assertion and Reason are true.

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF MATRICES AND DETERMINANTS

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE (II. Answer the following)|15 Videos

  • APPLICATIONS OF MATRICES AND DETERMINANTS

    PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 1.8|25 Videos

  • APPLICATIONS OF INTEGRATION

    PREMIERS PUBLISHERS|Exercise Answer the following questions.|18 Videos

  • APPLICATIONS OF VECTOR ALGEBRA

    PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE (Answer the following questions)|21 Videos

Similar Questions

Explore conceptually related problems

If A is a non-singular matrix then |A^(-1)| =

If A is a nonsingular matrix such that A A^(T)=A^(T)A and B=A^(-1) A^(T) , then matrix B is

If A is a symmetric matrix, B is a skew-symmetric matrix, A+B is nonsingular and C=(A+B)^(-1) (A-B) , then prove that (i) C^(T) (A+B) C=A+B (ii) C^(T) (A-B)C=A-B (iii) C^(T)AC=A

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

Let A be an orthogonal matrix, and B is a matrix such that AB=BA , then show that AB^(T)=B^(T)A .

If the elements of a matrix A are real positive and distinct such that det(A+A^(T))^(T)=0 then

If A is a 3xx3 non -singular matrix such that "AA"^(T)=A^(T)A "and" B=A^(-1)A^(T), "then" BB^(T) =

If A is non-singular and (A-2I)(A-4I)=O ,t h e n1/6A+4/3A^(-1) is equal to O I b. 2I c. 6I d. I

If A is non-singular and (A-2I)(A-4I)=O ,t h e n1/6A+4/3A^(-1) is equal to O I b. 2I c. 6I d. I

PREMIERS PUBLISHERS-APPLICATIONS OF MATRICES AND DETERMINANTS -PROBLEMS FOR PRACTICE (I. Choose the correct answer)
  1. Match the following :

    Text Solution

    |

  2. Find the incorrect statement in the following :

    Text Solution

    |

  3. Find the incorrect statement in the following :

    Text Solution

    |

  4. Find the correct statement :

    Text Solution

    |

  5. Find the odd one out :

    Text Solution

    |

  6. Find the odd one out : If A=|[3,7],[4,9]| then its inverse is :

    Text Solution

    |

  7. If A is a matrix of order (2xx3) then A^(-1) will be :

    Text Solution

    |

  8. Two matrices A and B equivalent. Find which is correct :

    Text Solution

    |

  9. If A=|[0,1,a],[1,a,0],[a,0,1]| is invertible matrix then a ne :

    Text Solution

    |

  10. If the system lambda x + 2y = mu and 7x+2y=5 have many solution is :

    Text Solution

    |

  11. The rank of [[1,2,3],[4,5,6]] is :

    Text Solution

    |

  12. Find the correct statement in the following :

    Text Solution

    |

  13. Which of the following is not an elementary transformation ?

    Text Solution

    |

  14. In a system equations if Delta = 0, then which of the following is tru...

    Text Solution

    |

  15. Which one of the following is the Echelon form :

    Text Solution

    |

  16. The inverse of A=[[cos theta, sin theta],[-sin theta,cos theta]] is :

    Text Solution

    |

  17. Find the correct pair from the following (i) In a system of equat...

    Text Solution

    |

  18. Find the odd one out :

    Text Solution

    |

  19. Find the incorrect pair of statements : (i) Two matrices A and B...

    Text Solution

    |

  20. Assertion : A matrix A is orthogonal if and only if A is non singular ...

    Text Solution

    |