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Math Help - Prove that matrix is invertible

  1. #1
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    israel
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    Prove that matrix is invertible

    Hi.
    I need to prove that if A^2+5A+6I=0 then A is invertibale.
    so im not sure if thats valid, but i think i can write it like that:
    (A+2I)(A+3I)=0

    but it still doesn't prove that A+2I=0 or A+3I=0, since they're bote can be zero divisors and therefore don't necessarily equal 0.

    so im kinda lost here.
    is there another way?

    TIA!
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  2. #2
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    Re: Prove that matrix is invertible

    from A2 + 5A + 6I = 0 we have:

    6I = -A2 - 5A

    I = (1/6)(-A - 5I)A

    so evidently, A-1 = (-1/6)(A + 5I)

    (not only is A invertible, we actually found the inverse!)
    Thanks from Stormey
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