Home
Class 11
MATHS
If for matrix A,A^(2)+l=0, where l is th...

If for matrix `A,A^(2)+l=0`, where l is the identity matrix, then A equals

A

`{:[(1,0),(0,1)]:}`

B

`{:[(-i,0),(0,-i)]:}`

C

`{:[(1,2),(-1,1)]:}`

D

`{:[(-1,0),(0,-1)]:}`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

  • MATRICES

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

  • LOGARITHMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|21 Videos

  • MEAN VALUE THEOREMS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|28 Videos

Similar Questions

Explore conceptually related problems

if for a matrix A, A^2+I=O , where I is the identity matrix, then A equals

If A is skew symmetric matrix, then I - A is (where I is identity matrix of the order equal to that of A)

Matrix A such that A^2=2A-I ,w h e r eI is the identity matrix, the for ngeq2. A^n is equal to 2^(n-1)A-(n-1)l b. 2^(n-1)A-I c. n A-(n-1)l d. n A-I

Matrix A such that A^2=2A-I ,w h e r eI is the identity matrix, the for ngeq2. A^n is equal to 2^(n-1)A-(n-1)l b. 2^(n-1)A-I c. n A-(n-1)l d. n A-I

If A=[1 2 2 2 1-2a2b] is a matrix satisfying the equation AA^T=""9I , where I is 3xx3 identity matrix, then the ordered pair (a, b) is equal to : (1) (2,-1) (2) (-2,""1) (3) (2, 1) (4) (-2,-1)

If B, C are square matrices of same order such that C^(2)=BC-CB and B^(2)=-I , where I is an identity matrix, then the inverse of matrix (C-B) is

If A=[(1, 0,-3 ),(2, 1 ,3 ),(0, 1 ,1)] , then verify that A^2+A=A(A+I) , where I is the identity matrix.

For a matrix A, if A^(2)=A and B=I-A then AB+BA +I-(I-A)^(2) is equal to (where, I is the identity matrix of the same order of matrix A)

Find all solutions of the matrix equation X^2=1, where 1 is the 2*2 unit matrix, and X is a real matrix,i.e. a matrix all of whose elements are real.

Show that thematrix A= [{:(,2,3),(,1,2):}] satisfies the equations A^(2)-4A+I=0 where I is 2 xx 2 identity matrix and O is 2 xx 2 zero matrix. Using the equations. Find A^(-1) .

OBJECTIVE RD SHARMA ENGLISH-MATRICES-Exercise
  1. Which of the following is/are incorrect? (i) adjoint of a symmetri...

    Text Solution

    |

  2. If [[alpha, beta], [gamma, -alpha]] is to be square root of two-rowed ...

    Text Solution

    |

  3. If for matrix A,A^(2)+l=0, where l is the identity matrix, then A equa...

    Text Solution

    |

  4. If A=[a(ij)](mxxn) is a matrix of rank r then (A) r=min{m,n} (B) rlemi...

    Text Solution

    |

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

    Text Solution

    |

  6. A=[a(ij)](mxxn) is a square matrix, if

    Text Solution

    |

  7. The rank of a null matrix is

    Text Solution

    |

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

    Text Solution

    |

  9. Which of the following is correct ?

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. If A is an orthogonal matrix, then

    Text Solution

    |

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

    Text Solution

    |

  15. Let A=[a(ij)](n xxn) be a square matrix and let c(ij) be cofactor of...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  19. Let A=[a(ij)](mxxn) be a matrix such that a(ij)=1 for all I,j. Then ,

    Text Solution

    |

  20. If A is a non-zero column matrix of order mxx1 and B is a non-zero row...

    Text Solution

    |