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Math Help - simetrix matrices determinant 2

  1. #1
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    simetrix matrices determinant 2

    A B are nXn order matrices
    1.if A^t=-A then det A=0
    2.if A B are simetric then AB is simetric too

    for each one of these is it true or false?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by transgalactic View Post
    A B are nXn order matrices
    1.if A^t=-A then det A=0
    False. It is only true if n is odd. For n even, take:

    A=\begin{bmatrix}{0}&{1}\\{-1}&{0}\end{bmatrix}

    2.if A B are simetric then AB is simetric too
    False. It is true if AB=BA. Try to find a counterexample.

    Regards.
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