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Math Help - Matrix equation

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    Matrix equation

    A is a 2x2 matrix, if A^{2}=0, then the matrix A may not be a zero matrix, right?

    Now if I have AB=0, then can I conclude that either A=0 or B=0?
    A and B can both be non-zero also, right?

    So then can I say that AB=0 implies A=0 or B=0 is not true in general? But when is it true, when is it not true?

    Thank you!!
    Last edited by acc100jt; July 12th 2010 at 05:55 AM.
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    MHF Contributor Also sprach Zarathustra's Avatar
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    Quote Originally Posted by acc100jt View Post
    A is a 2x2 matrix, if A^{2}=0, then the matrix A may not be a zero matrix, right?

    Now if I have AB=0, then can I conclude that either A=0 or B=0?
    A and B can both be non-zero also, right?

    So then can I say that AB=0 implies A=0 or B=0 is not true in general? But when is it true, when is it not true?

    Thank you!!
    Yes:

    For the first:

    0 1
    0 0

    second:
    A=
    0 0
    0 1

    B=
    0 1
    0 0
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