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Homework Help: Linear algebra proof

  1. Jan 26, 2013 #1
    1. The problem statement, all variables and given/known data

    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?


    2. Relevant equations

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


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    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


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    And (AB)-1 = B-1A-1, not A-1B-1
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