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Math Help - How to prove the determinant of a matrix is zero?

  1. #1
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    How to prove the determinant of a matrix is zero?

    The matrix M satisifies the following properties:
    1. m_{ii}>0
    2. m_{pq}m_{qp}=m_{pp}m_{qq}
    3. m_{ij}m_{ji}=0 or m_{ii}m_{jj}, i,j not equal to p and q.
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  2. #2
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    Do a row reduction: look at what happens when you subtract, say, \frac{a_{12}}{a_{11}} times the first row from the second. Try it with a 2 by 2 matrix first.
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  3. #3
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    Many thanks for your reply.

    It holds when M is a 2 by 2 matrix.

    I tried using row reduction, most items become same but there still exist some items uncertain.

    In fact, I am perplexed by this problem for such a long time and I have tried using induction but failed.
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