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Pleeeeaaseeee proofs in linear algebra

  1. Mar 29, 2009 #1
    1. The problem statement, all variables and given/known data

    1) (AB)^-1=A^-1B^-1 A and B are nonsingular nxn
    2) If A is nonsingular then A^-1 is nonsingular also and then (A^-1)^-1=A



    3. The attempt at a solution

    1) I do know that I have to multiply but I don´t know why. Can you tell me why??
    This is how I do it:
    ((AB)^-1)*(A^-1B^-1 ))A(BB^-1)A^-1=A*In*A^-1=A*A^-1=In

    2) ((A^-1)^-1)*A = ?????
     
  2. jcsd
  3. Mar 29, 2009 #2

    tiny-tim

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    Hi cleopatra! :smile:

    (try using the X2 tag just above the Reply box :wink:)
    :rolleyes: Your question is wrong … it should be prove (AB)-1 = B-1A-1
     
  4. Mar 29, 2009 #3
    ohh I see that now. Thanks :)
     
  5. Mar 29, 2009 #4
    can you maby help me? :biggrin:
     
  6. Mar 29, 2009 #5

    tiny-tim

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    well, to prove (AB)-1 = B-1A-1

    what is the definition of (AB)-1 ? :wink:
     
  7. Mar 29, 2009 #6
    the definition of (AB)-1 is
    that AB is the inverce of AB

    ?
     
  8. Mar 29, 2009 #7

    tiny-tim

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    Yes :rolleyes:, but what does that mean?
     
  9. Mar 29, 2009 #8
    it means that when I multiply it with AB I get In
    Right?
     
  10. Mar 29, 2009 #9

    tiny-tim

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    Right! :smile:

    And that's the way you answer any question …

    ask yourself what the definition is, and then prove that the definition fits …

    in this case, prove that when you multiply the answer by AB, you get In :wink:
     
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