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Math Help - matrices and determinants

  1. #1
    Junior Member
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    matrices and determinants

    Let A be an n x n matrix with A^2 - 4A + 5I=0?

    show that n must be even.
    it know you have to complete the square and take determinants but not sure how to do it

    thanks
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  2. #2
    MHF Contributor

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    Quote Originally Posted by b0mb3rz View Post

    Let A be an n x n matrix with A^2 - 4A + 5I=0. show that n must be even.

    it know you have to complete the square and take determinants but not sure how to do it

    thanks
    we have (A-2I)^2=-I and thus: (\det(A - 2I))^2=(-1)^n. i think you can finish the proof now.
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