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Proving Linear Algebra

  1. Apr 21, 2010 #1
    1. The problem statement, all variables and given/known data

    If A and B [tex]\in[/tex] Mn(R) and B is invertible

    show that

    l A-cI l = l B-1AB-cI l

    2. Relevant equations

    N/A

    3. The attempt at a solution

    i've no idea how to prove this. can give me any clue?

    l AI-cI l = l ABB-1-cI l

    am i in the right way?
     
  2. jcsd
  3. Apr 22, 2010 #2
    recall that for square matrices

    [tex]

    det(AB) = det(A)det(B)

    [/tex]

    and for an invertible square matrix,

    [tex]

    det(B^{-1}) = det(B)^{-1}

    [/tex]

    How can you apply these?
     
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