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: Linear Algebra.

  1. Nov 16, 2008 #1
    1. The problem statement, all variables and given/known data

    Show that if AAt(where At is the transpose of A) has no inverse,Then A itself cannot have an inverse

    2. The attempt at a solution

    Here's what i did


    thus AAt has an inverse IF and only IF A is invertible and since AAT has no inverse then A has no inverse ...

    i thinkt it's somehow wrong the teacher told me that i assumed that AAt is invertible but it's given without an inverse ..any suggestions would be appreciated :)
  2. jcsd
  3. Nov 16, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    You've assumed it's invertible by writing down (AAT)-1

    Hint: Consider determinants...
  4. Nov 16, 2008 #3
    i haven't taken determinant till now.. is there any other way to do it ?
  5. Nov 16, 2008 #4


    User Avatar
    Science Advisor

    You want to prove "If AAT does NOT have an inverse, then A itself does NOT have an inverse". With all those "not"s, that's what I would call a "negative" statement. It is almost easier to prove the contraposative of a "negative" statement than the statement itself because then you can make a "positive" statement.

    Here the contrapositive is "If A has an inverse then so does AAT."
  6. Nov 16, 2008 #5
    you mean i should assume that A is invertible and prove that AAT is invertible also ...
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook