Home
Class 12
MATHS
True or False statements : If and B ar...

True or False statements :
If and B are invertible matrices such that AB = BA, then `(AB)^-1 = A^-1B^-1`

Promotional Banner

Topper's Solved these Questions

  • DETERMINANTS

    PRADEEP PUBLICATION|Exercise EXERCISE|342 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    PRADEEP PUBLICATION|Exercise EXERCISE|788 Videos

  • DIFFERENTIAL EQUATIONS

    PRADEEP PUBLICATION|Exercise EXERCISE|507 Videos

Similar Questions

Explore conceptually related problems

True or False statements : If A and B are invertible matrices then AB is invertible and (AB)^-1 = B^-1 A^-1

If A and B are invertible matrices of the same order, then (AB)^-1 is equal to

True or False statements : If A and B are invertible matrices of he same order than A + B is also invertible.

Let A and B are two matrices such that AB = BA, then for every n in N

True or False statements : if A and B are square matrices of the same order then A - B = B - A.

True or False statements : If A,B,C are three matrices such that both AB and AC are defined and are equal, then it implies that B and C are equal matrices.

True or False statements : If A and B are non-zero square matrices of the same order then AB is also a non-zero matrix.

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

If AB=A and BA=B, then B^2 =

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

PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
  1. Without expanding, show that : Delta = {:|(cosec^2theta,cot^2theta,1...

    Text Solution

    |

  2. Evaluate the following determinants: {:|(x^2-x+1,x-1),(x+1,x+1)|

    Text Solution

    |

  3. True or False statements : If and B are invertible matrices such tha...

    Text Solution

    |

  4. If A and B are two square matrices of the same order, then AB=BA .

    Text Solution

    |

  5. If Delta=|{:(1,x,x^(2)),(1,y,y^(2)),(1,z,z^(2)):}| and Delta(1)=|{:(1,...

    Text Solution

    |

  6. If A is a square matrix of order 3 and |3A| = k|A|, then write the val...

    Text Solution

    |

  7. For what value of x is the matrix [(5-x,x+1),(2,4)] singular ?

    Text Solution

    |

  8. Find the minor of a23 in |(2,-3,5),(6,0,4),(1,5,-7)|

    Text Solution

    |

  9. Find the cofactor of a12 in |(2,-3,5),(6,0,4),(1,5,-7)|

    Text Solution

    |

  10. If |(x+1,x-1),(x-3,x+2)|=|(4,-1),(1,3)| find the value of x.

    Text Solution

    |

  11. Write the value of Delta = |(x+y, y +z , z +x),(z, x,y),(-3,-3,-3)|

    Text Solution

    |

  12. If A is a 3xx3 matrix and |3A | = k |A|, then write the value of k.

    Text Solution

    |

  13. For what value of 'k', the system of linear equations : x+y+z=2,2x+y...

    Text Solution

    |

  14. Evaluate the determinants in exercises 1 to 2. |(2,4),(-5,-1)|

    Text Solution

    |

  15. Evaluate the determinants in exercises 1 to 2. |(cos theta, - sin th...

    Text Solution

    |

  16. Evaluate the following determinants: {:|(x^2-x+1,x-1),(x+1,x+1)|

    Text Solution

    |

  17. If A =[{:(1,2),(4,2):}], then show that | 2A| = 4|A|.

    Text Solution

    |

  18. If A = [[1,0,1],[0,1,2],[0,0,4]] then show that |3A| = 27|A|

    Text Solution

    |

  19. Evaluate the following determinants: {:|(3,-1,-2),(0,0,-1),(3,-5,0)|

    Text Solution

    |

  20. Evaluate the determinant : |[3,-4,5],[1,1,-2],[2,3,1]|

    Text Solution

    |