1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Showing a matrix is invertible

  1. Feb 19, 2014 #1
    1. The problem statement, all variables and given/known data

    let A and B be nXn invertible matrices. Show that (A.B)T is invertible by finding it's inverse

    2. Relevant equations

    3. The attempt at a solution

    Last edited: Feb 19, 2014
  2. jcsd
  3. Feb 19, 2014 #2


    User Avatar
    Gold Member

    You are looking for a matrix ##C## such that ##(AB)^{T}C = C(AB)^T = I_{n}##. The question does not say that A and B are invertible, however given that the inverse of (AB)T exists you can show that they are indeed invertible.
  4. Feb 19, 2014 #3
    Sorry I left out the fact that A and B are invertible.
  5. Feb 19, 2014 #4


    User Avatar
    Science Advisor

    You have already said that [itex](AB)^T= B^TA^T[/itex]. Okay, what will get rid of that [itex]B^T[/itex] and then what will get rid of that [itex]A^T[/itex]

    (Of course, you know that a matrix is invertible if and only if its determinant is not 0? And that the determinant of [itex]X^T[/itex] is the same as the determinant of [itex]X[/itex]?)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted