Results 1 to 3 of 3

Math Help - Matrices and inverses

  1. #1
    Senior Member I-Think's Avatar
    Joined
    Apr 2009
    Posts
    288

    Matrices and inverses

    Let A and B be n*n matrices and let their product AB be invertible.
    Prove A and B are invertible
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Lord of certain Rings
    Isomorphism's Avatar
    Joined
    Dec 2007
    From
    IISc, Bangalore
    Posts
    1,465
    Thanks
    6

    Re: Matrices and inverses

    Quote Originally Posted by I-Think View Post
    Let A and B be n*n matrices and let their product AB be invertible.
    Prove A and B are invertible
    Let C be the inverse of AB, then C(AB) = (AB)C = I.
    Now use associativity in the above expression. do you see it?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member Tinyboss's Avatar
    Joined
    Jul 2008
    Posts
    433

    Re: Matrices and inverses

    Another way to see why it "should be" true is to consider the identity det(AB)=det(A)det(B). Isomorphism's answer is definitely more straightforward, though.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Inverses of matrices
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: January 24th 2011, 07:34 AM
  2. Matrices which are their own inverses
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: February 19th 2009, 10:51 PM
  3. matrices, inverses, transposes, r.r.e.f...
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: February 15th 2009, 07:02 AM
  4. Matrices and Inverses - Generalizing?
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 22nd 2009, 10:36 PM
  5. inverses of matrices
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 26th 2007, 12:05 PM

Search Tags


/mathhelpforum @mathhelpforum