Results 1 to 4 of 4

Math Help - Inverses

  1. #1
    Junior Member
    Joined
    Feb 2010
    Posts
    43

    Inverses

    Hi,

    Why is it that if B = A^-1,

    B^-1 = A


    I understand that whatever you do to one side, you have to do the same for the other side, but I don't understand how (B^-1)(B^-1) = B

    Can anyone please explain?

    Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member jakncoke's Avatar
    Joined
    May 2010
    Posts
    387
    Thanks
    80
    What is this in regards to? What field are we working in? Matricies?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by CSG18 View Post
    Hi,

    Why is it that if B = A^-1,

    B^-1 = A

    I understand that whatever you do to one side, you have to do the same for the other side, but I don't understand how (B^-1)(B^-1) = B

    Can anyone please explain?

    Thanks.
    B^{-1} = (A^{-1})^{-1} = A.

    Alternatively, note that B B^{-1} = I. But if B = A^{-1} then A^{-1} B^{-1} = I \Rightarrow A  A^{-1} B^{-1} = A \Rightarrow I B^{-1} = A ....
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,427
    Thanks
    1857
    The definition of X^{-1}, in general, (matrices, elements of a group or field, etc.) is that Y= X^{-1} if and only if XY= I and YX= I where I is the "multiplicative identity" for the algebraic structure. T

    If you know that B= A^{-1} then you know that AB= I and [mathy]BA= I[/tex], by replacing X above with A and Y with B. But if we were to replace X with B and Y with A, we wold get exactly the same equations!

    Therefore, A= B^{-1}.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Inverses
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: November 11th 2010, 03:49 PM
  2. Inverses
    Posted in the Algebra Forum
    Replies: 4
    Last Post: February 11th 2010, 12:17 AM
  3. Right inverses
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: November 19th 2008, 12:38 PM
  4. inverses......
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: May 24th 2008, 05:12 AM
  5. Inverses
    Posted in the Calculus Forum
    Replies: 6
    Last Post: December 10th 2007, 05:37 AM

Search Tags


/mathhelpforum @mathhelpforum