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Homework Help: Linear algebra problem

  1. Nov 21, 2008 #1
    1. The problem statement, all variables and given/known data
    Let A and B be two n x n matrices that are related by the equation (P^-1)(A)(P) = B, where P is another n x n matrix. Prove that det(A) = det(B).

    2. Relevant equations

    3. The attempt at a solution
    I'm thinking the first step might be to come up with general forms of A and B that are related by the above equation? I've been trying to do that and not been successful so far. Any ideas? thanks
  2. jcsd
  3. Nov 21, 2008 #2


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    Staff Emeritus
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    Why not just 'compute' det(B)?
  4. Nov 21, 2008 #3
    Two basic facts you should know (and use them in this exercise):
    The equality
    is true for any two nxn matrices.
    And we have for any invertible matrix
    det(A^-1)= ???
    (I think you should be able to guess the result using the definition of the inverse and the above equation.)
    That's all you need to know in order to solve this one.
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