Home
Class 14
MATHS
Consider the following statements with r...

Consider the following statements with respect to the square matrices A and B of same order
I. A and B are non-zero and `AB = 0 rArr` either |A|=0 or |B|=0
II. `AB=0 rArr A=0" or B=0`
Which of the above statements is/are correct ?

A

Only I

B

Only II

C

Both I and II

D

Neither I nor II

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • MATRIX

    PUNEET DOGRA|Exercise PREV YEAR QUESTIONS|91 Videos

  • LOGARITHM

    PUNEET DOGRA|Exercise PREVIOUS YEAR QUESTIONS|24 Videos

  • PERMUTATION AND COMBINATION

    PUNEET DOGRA|Exercise PREV YEAR QUESTIONS|50 Videos

Similar Questions

Explore conceptually related problems

Consider the following statements in respect of the square matrices A and B of same order: 1. A and B are non-zero and AB = 0 rarr either |A| = 0 or |B| = 0 2. AB = 0 rarr A = 0 or B = 0 Which of the above statements is/are correct ?

Give examples of two square matrices A and B of the same order for which AB=0, but BA!=0

If A and B are square matrices of same order such that AB=O and B ne O , then prove that |A|=0 .

Consider the following statements. I. The inverse of the square matrix, if it exits, is unique. II. If A and B are singular matrices of order n. then AB is also a singular matrix of order n. Which of the statements given above is/are correct ?

Consider the following statements in respect of the matrix A=[{:(0,1,2),(-1,0,-3),(-2,3,0):}] I. The matrix A is skew symmetric II. The matrix A is symmetric III. The matrix A is invertible Which of the above statements is/are correct ?

If A and B are square matrices of the same order and AB=3I , then A^(-1)=

If A, B are square matrices of order 3, A is non-singular and AB=0, then B is a

Consider the following statements. I. The inverse of a square matrix, if it exists, is unique. II. If A and B are singular matrices of order n, then AB is also a singular matrix of order n. Which of the statements given above is/are correct ?

Consider the following in respect of matrices A and B of same order: I. A^(2)-B^(2)=(A+B)(A-B) II. (A-I) (I+A)=0 rArr A^(2) =I Where I is the identity matrix and O is the null matrix. Which of the above is/are correct ?

A and B are two square matrices of same order. If AB =B^(-1), " then " A^(-1) =____.

PUNEET DOGRA-MATRIX-PREV YEAR QUESTIONS
  1. If A is a square matrix such that A^(2)=l where l is the identity matr...

    Text Solution

    |

  2. What is the order of : [xyz] [{:(a,h,g),(h,b,f),(g,f,c):}][{:(x),(y),(...

    Text Solution

    |

  3. Then sum and product of matrices A and B exist. Which of the following...

    Text Solution

    |

  4. If A=[{:(1,2),(1,1):}] and B = [{:(0,-1),(1,2):}] , then what is the v...

    Text Solution

    |

  5. Consider the following statements with respect to the square matrices ...

    Text Solution

    |

  6. For what value of x does {:(1  {:3 &nbsp {:2:})({:(1,3,0),(3,0,2),(2,0...

    Text Solution

    |

  7. If the matrix A=[{:(2-x,1,1),(1,3-x,0),(-1,-3,-x):}] is singular then ...

    Text Solution

    |

  8. If A=[{:(alpha,0),(1,1)] and B=[{:(1,0),(2,1):}] such that A^(2)=B the...

    Text Solution

    |

  9. If A=[{:(3,1),(0,4):}] and B = [{:(1,1),(0,2):}], then which of the fo...

    Text Solution

    |

  10. If [{:(1,-3,2),(2,-8,5),(4,2, lamda):}] is not an invertible matrix, t...

    Text Solution

    |

  11. Consider the following statements. I. The inverse of the square matr...

    Text Solution

    |

  12. If the matrix A=[{:(alpha, beta),(beta,alpha):}] is such that A^(2)=I,...

    Text Solution

    |

  13. Let A and B matrices of order 3xx3 If AB=0. then which of the followin...

    Text Solution

    |

  14. Consider the following statements in respect of a square matrix A and ...

    Text Solution

    |

  15. If A=[{:(0,1),(-1,0):}] B=[{:(i,0),(0,-i):}] C=[{:(0,-i),(-i,0):}] the...

    Text Solution

    |

  16. If A is a square matrix, then the value of adj A^(T)-(adj A)^(T) is eq...

    Text Solution

    |

  17. If a matrix A is such that 3A^(3)+2A^(2)+5A+1=0. Then A^(-1) is equal ...

    Text Solution

    |

  18. Let A [{:(5,6,1),(2,-1,5):}], if there exists a matrix B such that AB ...

    Text Solution

    |

  19. Consider the following statements: I. If A=A. then A is singular mat...

    Text Solution

    |

  20. Let A=[(1,2),(3,4)], [a(ij)] where I,j =1,2. If its inverse matrix is ...

    Text Solution

    |