Home
Class 11
MATHS
If A is an invertible matrix and A is a...

If A is an invertible matrix and A is also invertible then prove `(A^(T))^(-1) = (A^(-1))`

Promotional Banner

Topper's Solved these Questions

  • MATRICES

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise TEXTUAL EXERCISES (EXERCISE -3( i))|4 Videos
  • MATHEMATICAL INDUCTION

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise Exercise 2 (a)|15 Videos
  • PAIR OF STRAIGHT LINES

    VIKRAM PUBLICATION ( ANDHRA PUBLICATION)|Exercise EXERCISE - 4(c) III. |3 Videos

Similar Questions

Explore conceptually related problems

If [(a,b),(c,d)] is invertible then

Let A and B be invertible matrices then prove that (AB)^-1=B^-1A^-1 .

Inverted sugar is

Inverted sugar is

If A, B are two invertible matrices of same type then (AB)^(-1)=

If A is a non-singular matrix then prove that A^(-1) = (adjA)/(|A|) .

If A is square matrix then A A^(T) is . . . . Matrix

If A is any matrix, then: (A^(T))^(T) =A

If A is an invertible matrix of order n, then the determinant of adj A is equal to

VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-MATRICES -SOLVED PROBLEMS
  1. Fiind the valueof x if: |{:(x-2, 2x-3, 3x-4),(x-4, 2x-9, 3x-16),(x-8...

    Text Solution

    |

  2. Find the Adjoint and Inverse of the matrix A = [(1,2),(3,-5)]

    Text Solution

    |

  3. Find the adjoint and the inverse of the matrix A=[{:(1,3,3),(1,4,3),(1...

    Text Solution

    |

  4. Show that the matrix A=[{:(1,2,1),(3,2,3),(1,1,2):}] is non-singular a...

    Text Solution

    |

  5. Find the rank of A=[{:(0,1,2),(1,2,3),(3,2,1):}] using elementary tran...

    Text Solution

    |

  6. Find the rank of A=[{:(1,2,0,-1),(3,4,1,2),(-2,3,2,5):}] using element...

    Text Solution

    |

  7. Apply the test of rank to examine whether the following equations are ...

    Text Solution

    |

  8. Solve the following system of equations by using Cramer,s ruel . 3x...

    Text Solution

    |

  9. Solve the equations 3x+4y+5z=18,2x+y+8z=13,5x-2y+7z=20 by matrix inver...

    Text Solution

    |

  10. Solve the following system of equations by using Cramer,s ruel . 3x...

    Text Solution

    |

  11. Solve the system of equations 2x+4y-z=0,x+2y+2z=5,3x+6y-7z=2 by Gauss ...

    Text Solution

    |

  12. Solve the following- system of equations, 2x + 5y + 6z = 0, x - 3y + 8...

    Text Solution

    |

  13. The number of nontrivial solutions of the system: x-y+z=0, x+2y=0, 2x+...

    Text Solution

    |

  14. Theorem: Matrix multiplication is associative, i.e., if conformability...

    Text Solution

    |

  15. Theorem : Matrix multiplication, is distri-butive over matrix addition...

    Text Solution

    |

  16. If A is any matrix, then: (A^(T))^(T) =A

    Text Solution

    |

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

    Text Solution

    |

  18. If A and B are two matrices for which conformability for multiplicatio...

    Text Solution

    |

  19. If A is an invertible matrix and A is also invertible then prove (A^(...

    Text Solution

    |

  20. A certain book shop has 10 dozen chemistry books, 8 dozen physics book...

    Text Solution

    |