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Homework Help: Determinants and Eigenvalues

  1. Oct 28, 2009 #1
    1. The problem statement

    For integers m >= n,

    Prove det(xIm - AB) = xm-ndet(xIn - BA) for any x in R.

    2. Relevant equations

    A is an m x n matrix
    B is an n x m matrix

    3. The attempt at a solution

    I tried working out the characteristic polynomials by hand but it just seems too tedious for a nice proof. I know that each x is an eigenvalue of AB but after that I'm stumped.
  2. jcsd
  3. Oct 28, 2009 #2
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