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!

Linear algebra proof

  1. Jan 26, 2013 #1
    1. The problem statement, all variables and given/known data
    http://i48.tinypic.com/2qu14ax.jpg

    Can you guys explain whether or not my proof would be sufficient. My thought process was to start with the definition.

    So if A is nonsingular is means that A has an inverse such that

    A=A-. I used that same thinking for B. B=B-

    Then using the question which states. IF A and B are nonsingular nxn matrices then AB is also nonsingular and (AB)-=A-B-

    I thought it would be easier to prove the right side so I started with AB=A-B-

    and used the relationship A=A- and B=B- to show that both sides are equal. However I found the proof online, and they did something slightly different.

    Am I incorrect, if so where did I go wrong in my thinking?

    Thanks


    2. Relevant equations



    3. The attempt at a solution
     
    Last edited by a moderator: Jan 26, 2013
  2. jcsd
  3. Jan 26, 2013 #2

    dx

    User Avatar
    Homework Helper
    Gold Member

    Non-singular does not mean that A = A-1

    It means that there is an inverse A-1 such that AA-1 = A-1A = I
     
  4. Jan 26, 2013 #3

    dx

    User Avatar
    Homework Helper
    Gold Member

    And (AB)-1 = B-1A-1, not A-1B-1
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Linear algebra proof
  1. Linear Algebra Proof (Replies: 8)

  2. Linear Algebra proof (Replies: 21)

Loading...