Home
Class 11
MATHS
If A and B are matrices such that AB = O...

If A and B are matrices such that AB = O then

A

`A=O,B!=O`

B

`A!=O,B=O`

C

`A=O,B=O`

D

A, B need not be null matrices

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    AAKASH SERIES|Exercise ALGEBRA OF MATRICES - EXERCISE - II|34 Videos
  • MATRICES

    AAKASH SERIES|Exercise ALGEBRA OF MATRICES -PRACTICE EXERCISE|41 Videos
  • MATRICES

    AAKASH SERIES|Exercise ADDITIONAL EXERCISE|51 Videos
  • MATHEMATICAL INDUCTION

    AAKASH SERIES|Exercise PRACTICE SHEET (EXERCISE-I) LEVEL-I (Principle of Mathematical Induction) (Straight Objective Type Questions)|55 Videos
  • MAXIMA & MINIMA

    AAKASH SERIES|Exercise EXERCISE-III|35 Videos

Similar Questions

Explore conceptually related problems

If A and B are two matrices such that AB and A+B are both defined, then A and B are

If A and B are two square matrices such that B=-A^(-1)BA then (A+B)^(2)=

If A,b are two square matrices such that AB=A,BA=B then A,B are

If A, B are two square matrices such that AB=B, BA=A and n in N then (A+B)^(n)=

If A and B are symmetric matrices then ABA is

If A-and B are two matrices of same type, then (A+B)^(T) =A^(T) + B^(T)

If A and B are two symmetric matrices then AB + BA is

If A and B are symmetric matrices of the same order, then show that AB is symmetric if and only if A and B commute, that is AB = BA.

If A and B are symmetric matrices, prove that AB-BA is a skew symmetric matrix.

If A and B are square matrices of the same order such that AB = BA, then prove by induction that AB^(n)=B^(n)A . Further, prove that (AB)^(n)=A^(n)B^(n) for all n in N .

AAKASH SERIES-MATRICES -ALGEBRA OF MATRICES -EXERCISE - I
  1. If A=[(4,1,0),(1,-2,2)],B=[(2,0,-1),(3,1,4)],C=[(1),(2),(-1)] and (3B-...

    Text Solution

    |

  2. If A=((2,3),(0,4))then A^(2)-5I=

    Text Solution

    |

  3. If A and B are matrices such that AB = O then

    Text Solution

    |

  4. A=[(-1,0),(0,2)]impliesA^(3)-A^(2)=

    Text Solution

    |

  5. A=[{:(1,2,2),(2,1,2),(2,2,1):}], then A^(3) - 4A^(2) -6A is equal to

    Text Solution

    |

  6. If A=[a(ij)] is scalar matrix then the trace of A is

    Text Solution

    |

  7. Find the trace of [(1,3,-5),(2,-1,5),(2,0,1)]

    Text Solution

    |

  8. If the trace of A is 7 then the trace of 7A is

    Text Solution

    |

  9. If A is a skew symmetric matrix, then trace of A is

    Text Solution

    |

  10. If A=[a(ij)] is a scalar matrix of order nxxn such that a(ii)=k for al...

    Text Solution

    |

  11. If the traces of A are 19 and B are 8 then the trace of A-B is

    Text Solution

    |

  12. If tr(A)=2+i then tr((2-i)A)=

    Text Solution

    |

  13. If tr(A)=3,tr(B)=5 then tr(AB)=

    Text Solution

    |

  14. If A=[(4,x+2),(2x-3,x+1)] is symmetric then trace of A is

    Text Solution

    |

  15. If A=[(x,1,4),(-1,0,7),(-4,-7,0)] such that A'=-A then x=

    Text Solution

    |

  16. P+Q=((2,3,5),(4,1,2),(1,2,1)),P is symmetric, Q is a skew symmetric ma...

    Text Solution

    |

  17. If 3A+4B'=[(7,-10,17),(0,6,31)],2B-3A'=[(-1,18),(4,-6),(-5,-7)] then B...

    Text Solution

    |

  18. If A=[(cos theta, sin theta, 0),(-sin theta, cos theta, 0),(0,0,1)] th...

    Text Solution

    |

  19. If 3A=[(-1,2,2),(2,-1,2),(2,2,-1)] then

    Text Solution

    |

  20. If A=[(2,x-3,x-2),(3,-2,-1),(4,-1,-5)] is a symmetric matrix then x =

    Text Solution

    |