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Math Help - Inverse matrix problem

  1. #1
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    Inverse matrix problem

    I'm having trouble with this question

    A^2 + 3A - 6I = 0 where A is a square matrix.
    Explain why A inverse exists and find it in terms of A.

    EDIT: Looking around it seems this thread would have been more suitable for the Linear algebra section. Could someone move it? Thanks.
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  2. #2
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    Quote Originally Posted by dvdy View Post
    I'm having trouble with this question

    A^2 + 3A - 6I = 0 where A is a square matrix.
    Explain why A inverse exists and find it in terms of A.

    EDIT: Looking around it seems this thread would have been more suitable for the Linear algebra section. Could someone move it? Thanks.

    A matrix is singular (= non-invertible) iff zero is one of its eigenvalues iff its characteristic polynomial has free coefficient equal to zero.

    Since x^2+3x-6 is a polynomial which vanishes at A we then know that the minimal pol. of A divides it, and since the min. pol. and the char. pol. of A have both exactly the same irreducible factors then...

    Tonio
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