Home
Class 12
MATHS
If A is a non-diagonal involutory matrix...

If A is a non-diagonal involutory matrix, then

A

`A-I=O`

B

`A+I=O`

C

`A-I` is nonzero singular

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`A^(2)=I`
or `A^(2)-I=O`
or `(A+I) (A-I)=0`
therefore, either `|A+I|=0` or `|A-I|=0`. If `|A-I| ne 0`, then `(A+I) (A-I)=Oimplies A+I=O` which is not so.
`:. |A-I|=0` and `A-I ne O`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    CENGAGE|Exercise Exercise (Multiple)|33 Videos

  • MATRICES

    CENGAGE|Exercise Exercise (Comprehension)|18 Videos

  • MATRICES

    CENGAGE|Exercise Exercise 13.5|17 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

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

If X is a non-zero column matrix, such that A X=lambda X where lambda is a scalar and the matrix A is [[4,6,6],[1,3,2],[-1,-5,-2]] then sum of distinct values of lambda is

If A is a non-singular matrix of odd order them

If A is a non-singular matrix such that A^(-1)=[(5,3),(-2,-1)], "then" (A^(T))^(-1) =

If A is a non - singular matrix of odd order, prove that |adj A| is positive.

If A is a non singular matrix such that A^(-1)=[[7,-2],[-3,1]] then (A^(T))^(-1) is :

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

CENGAGE-MATRICES-Exercise (Single)
  1. if Aa n dB are squares matrices such that A^(2006)=Oa n dA B=A+B ,t h ...

    Text Solution

    |

  2. If matrix A is given by A=[[6,11] , [2,4]] then determinant of A^(2005...

    Text Solution

    |

  3. If A is a non-diagonal involutory matrix, then

    Text Solution

    |

  4. If A and B are two nonzero square matrices of the same order such that...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  8. Which of the following is an orthogonal matrix ?

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. If A(alpha, beta)=[("cos" alpha,sin alpha,0),(-sin alpha,cos alpha,0),...

    Text Solution

    |

  14. If A=[(a+ib,c+id),(-c+id,a-ib)] and a^(2)+b^(2)+c^(2)+d^(2)=1, then A^...

    Text Solution

    |

  15. Id [1//25 0x1//25]=[5 0-a5]^(-2) , then the value of x is a//125 b. 2a...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  18. If A and B are two square matrices such that B=-A^(-1)BA, then (A+B)^(...

    Text Solution

    |

  19. A=[[1, tan x],[-tan x,1]], show that A^(T)A^(-1)=[[cos 2x,-sin 2x],[si...

    Text Solution

    |

  20. If A is order 3 square matrix such that |A|=2, then |"adj (adj (adj A)...

    Text Solution

    |