Home
Class 12
MATHS
Give examples of matrices A and B suc...

Give examples of matrices `A` and `B` such that `A B=O` but `B A!=O` . (ii) `A ,\ B` and `C` such that `A B=A C` but `B!=C ,\ A!=O` .

Text Solution

Verified by Experts

`A=[[1, 0], [0,0]]`, `B=[[1, 1], [1, 0]]` and `C=[[1, 1], [1, 2]]`
`AB=[[1, 1], [0, 0]]`
`AC=[[1, 1], [0, 0]]`
`AB=AC` but `B!=C`
Promotional Banner

Topper's Solved these Questions

  • ADJOINTS AND INVERSE OF MATRIX

    RD SHARMA|Exercise QUESTION|1 Videos

  • ALGEBRA OF VECTORS

    RD SHARMA|Exercise Solved Examples And Exercises|331 Videos

Similar Questions

Explore conceptually related problems

Give an example of three matrices A,B,C such that AB=AC but B!=C .

Give examples of matrices A and B such that AB!=BA.( ii) A and B such that AB=O but A!=O,B!=O

Give an example of two matrices A and B such that A!=O,B!=O,AB=O and BA!=O (ii) A!=O,quad B!=O,AB=BA=O

Let A = ((a,b),(c,d)) be such that A^(3)=O but Ane O then

If B is an idempotent matrix,and A=I-B then a.A^(2)=A b.A^(2)=I c.AB=O d.BA=O

If A and B are square matrices such that A^(2020)=O and AB=A+B , then |B| is equal to (where, O is a null matrix)

In Fig. 9.25, diagonals AC and BD of quadrilateral ABCD intersect at O such that O B" "=" "O D . If A B" "=" "C D , then show that: (i) a r" "(D O C)" "=" "a r" "(A O B) (ii) a r" "(D C B)" "=" "a r" "(A C B) (iii) D A" "||" "C

Diagonals A C a n d B D of a quadrilateral A B C D intersect at O in such a way that a r ( A O D)=a r ( B O C)dot Prove that A B C D is a trapezium.

A B C D is a trapezium such that B C || A D and A B=4c m . If the diagonals A C and B D intersect at O such that (A O)/(O C)=(D O)/(O B)=1/2 , then B C= 7c m (b) 8c m (c) 9c m (d) 6c m

if A and B are squares matrices such that A^(2006)=O and AB=A+B, then det (B) equals 0 b.1 c.-1 d.none of these

RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
  1. A matrix X has a+b rows and a+2 columns while the matrix Y has b+1 ...

    Text Solution

    |

  2. Give examples of matrices A and B such that A B!=B A . (ii) A and B...

    Text Solution

    |

  3. Give examples of matrices A and B such that A B=O but B A!=O . (ii)...

    Text Solution

    |

  4. Let A and B be square matrices of the same order. Does (A+B)^2=A^2+...

    Text Solution

    |

  5. If A and B are square matrices of the same order, explain, why in g...

    Text Solution

    |

  6. Let A and B be square matrices of the order 3xx3 . Is (A B)^2=A^2B^...

    Text Solution

    |

  7. If A and B are square matrices of the same order such that A B=B A ...

    Text Solution

    |

  8. Let A=[1 1 1 3 3 3] , B=[3 1 5 2-2 4] and C=[4 2-3 5 5 0] . Verify tha...

    Text Solution

    |

  9. Three shopkeepers A ,\ B\ a n d\ C go to a store to buy stationary....

    Text Solution

    |

  10. The cooperative stores of a particular school has 10 dozen physics ...

    Text Solution

    |

  11. In a legislative assembly election, a political group hired a publi...

    Text Solution

    |

  12. A trust fund has Rs. 30000 that must be invested in two different t...

    Text Solution

    |

  13. To promote making of toilets for women, an organisation tried to ge...

    Text Solution

    |

  14. There are two families A and B.In family A, there are 4 men, 6 women a...

    Text Solution

    |

  15. In a parliament election, a political party hired a public relation...

    Text Solution

    |

  16. The monthly incomes of Aryan and Babban are in the ratio 3 : 4 and ...

    Text Solution

    |

  17. A trust invested some money in two types of bonds. The first bond pays...

    Text Solution

    |

  18. If A=[-1 2 3] and B=[-2\ \ -1\ \ -4] , verify that (A B)^T=B^T\ A^T

    Text Solution

    |

  19. If A=[costheta-sinthetasinthetacostheta] , then find the values of ...

    Text Solution

    |

  20. If A=[(1,2,2),(2,1,-2),(a,2,b)] is a matrix satisfying "AA"^T=9I3 , th...

    Text Solution

    |