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Math Help - Matrices problem

  1. #1
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    Matrices problem

    Hi, I'm having trouble figuring this out:
    A is an nxn matrix. It's given that A2=A, A=\=0, A=\=I (I is nxn)
    prove or disprove: Ax=0 has only the trivial solution
    I tried to disprove that with the determinant:
    det(A2)=det(A)
    2det(A)=det(A)
    det(A)=0
    Hence A is singular
    BUT im not sure that this det(A2)=2det(A) is right, and I can't fathom why A=\=0, A=\=I (I is nxn) is given, so I suspect I'm mistaken.
    help is very welcomed
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  2. #2
    Member ModusPonens's Avatar
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    Re: Matrices problem

    Your solution is incorrect, because det(A^2)=det(A)^2. But this is the right track. Can you follow from here?
    Thanks from ineedhelplz
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  3. #3
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    Re: Matrices problem

    consider A =

    [1 0]
    [0 0].
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  4. #4
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    Re: Matrices problem

    Thanks to the both of you!
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