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Math Help - Matrixes Arithmetic

  1. #1
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    Matrixes Arithmetic

    Show that if a square matrix A satisfies A^2 - 3A + I = 0 then A^-1 = 3I - A

    I tried to solve from a series of equations, but it just went in circles.
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  2. #2
    Senior Member Dinkydoe's Avatar
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    Given is: A^2-3A+I = 0 \Longrightarrow I = -A^2+ 3A

    Now observe that A(3I-A) = -A^2+3A = I . Hence A^{-1} = 3I-A
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