Home
Class 12
MATHS
Matrix A ha s m rows and n+ 5 columns; m...

Matrix A ha s m rows and n+ 5 columns; matrix B has m rows and `11 - n` columns. If both AB and BA exist, then (A) AB and BA are square matrix (B) AB and BA are of order `8 xx 8` and `3 xx 13`, respectively (C) `AB=BA` (D) None of these

Text Solution

Verified by Experts

If both AB and BA exist, then the number of columns of A is equal to the number of rows of B. Therefore,
`n+5=m` (1)
And the number of columns of B is equal to the number of rows of A. therefore,
`11-n=m` (2)
Solving (1) and (20, we get `n=3` and `m=8`. Hence, A has order `8xx8` has order `8xx8`. Hence, both AB and BA are square matrices.
Promotional Banner

Topper's Solved these Questions

  • MATHMETICAL REASONING

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

  • METHODS OF DIFFERENTIATION

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|7 Videos

Similar Questions

Explore conceptually related problems

If A and B are square matrices of the same order such that AB = A and BA = B, then……

If A and B are n-rowed unitary matrices,then AB and BA are also unitary matrices.

if A and B are two matrices of order 3xx3 so that AB=A and BA=B then (A+B)^7=

A and B arer two matrices of order 3 × 3 which satisfy AB = A and BA = B. then (A+I)^(5) is equal to (where I is identify matrix)___

If A and B are square matrices of the same order such that A^(2)=A,B^(2)=B,AB=BA=0 , then__

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

If A and B are two square matrices of order 3xx3 which satify AB=A and BA=B , then Which of the following is true ?

The order of the matrix A is 3×5 and that of order B is 2×3 then the order of matrix BA is

If A and B are two square matrices of order 3xx3 which satify AB=A and BA=B , then (A+I)^(5) is equal to (where I is idensity matric)

If A and B are square matrices of same order such that AB+BA=O , then prove that A^(3)-B^(3)=(A+B) (A^(2)-AB-B^(2)) .

CENGAGE PUBLICATION-MATRICES-All Questions
  1. If [(lambda^(2)-2lambda+1,lambda-2),(1-lambda^(2)+3lambda,1-lambda^(2)...

    Text Solution

    |

  2. Prove that every square matrix can be uniquely expressed as the sum of...

    Text Solution

    |

  3. Matrix A ha s m rows and n+ 5 columns; matrix B has m rows and 11 - n ...

    Text Solution

    |

  4. If A=[{:(2,3,-1),(1,4,2):}] and B=[{:(2,3),(4,5),(2,1):}] then prove t...

    Text Solution

    |

  5. Find the value of x and y that satisfy the equations [(3,-2),(3,0),(2,...

    Text Solution

    |

  6. Find the values of x ,\ y,\ z if the matrix A=[(0,2y,z), (x, y,-z ),...

    Text Solution

    |

  7. If A =[[costheta,sintheta],[-sintheta,costheta]] then prove that A^n=[...

    Text Solution

    |

  8. If A=((p,q),(0,1)), then show that A^(8)=((p^(8),q((p^(8)-1)/(p-1))),(...

    Text Solution

    |

  9. Let A=[(2,1),(0,3)] be a matrix. If A^(10)=[(a,b),(c,d)] then prove th...

    Text Solution

    |

  10. Show that the solutions of the equation [(x,y),(z,t)]^2=0 are[(x,y),(...

    Text Solution

    |

  11. Let A be square matrix. Then prove that A A^(T) and A^(T) A are symmet...

    Text Solution

    |

  12. If A, B are square materices of same order and B is a skewsymmetric ma...

    Text Solution

    |

  13. If A and B are square matrices of same order such that AB+BA=O, then p...

    Text Solution

    |

  14. Let A=[(1,2),(-1,3)] .If A^6=kA-205I then find the numerical quantit...

    Text Solution

    |

  15. Let A, B, C, D be (not necessarily square) real matrices such that A^T...

    Text Solution

    |

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

    Text Solution

    |

  17. If A=[-1 1 0-2] , then prove that A^2+3A+2I=Odot Hence, find Ba n dC m...

    Text Solution

    |

  18. If A=[(3,-4),(1,-1)] then find tr. (A^(2012)).

    Text Solution

    |

  19. If A is a nonsingular matrix satisfying AB-BA=A, then prove that det. ...

    Text Solution

    |

  20. If det, (A-B) ne 0, A^(4)=B^(4), C^(3) A=C^(3)B and B^(3)A=A^(3)B, the...

    Text Solution

    |