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Thread: matrix problem

  1. #1
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    matrix problem

    Someone please help to solve this.
    Let A be an nxn matrix and n is odd. Show that it is not possible for A2 + I = O.
    And what about n is even?
    Last edited by alter027; Dec 19th 2016 at 06:12 PM.
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  2. #2
    MHF Contributor
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    Re: matrix problem

    show your work so far

    additionally you might want to restrict $A_{i,j} \in \mathbb{R}$

    otherwise

    $A=i I_{n,n}$

    $A^2 + I = 0$
    Last edited by romsek; Dec 19th 2016 at 06:30 PM.
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  3. #3
    Senior Member zzephod's Avatar
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    Re: matrix problem

    For $n$ even a single example will suffice to show it is possibbe for an $n\times n$ matrix $A$ to satisfy $A^2+1=0$. Trial and error or playing with the possibilities will allow you to find a $2 \times 2$ matrix with the required property.
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