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Property of determinants

  1. Apr 14, 2012 #1
    Hi. I have the following sentence:

    [tex]\begin{array}{l}
    A,B \in {M_{nxn}}\\
    A \ne 0\\
    B \ne 0\\
    {\rm{if }}AB = 0{\rm{ then}}\\
    {\rm{|A| = 0 or |B| = 0}}
    \end{array}[/tex]

    I know this is true but how can I realize? Just thinking about an example?


    Thanks!
     
  2. jcsd
  3. Apr 14, 2012 #2

    morphism

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    Can you express the determinant of AB in terms of those of A and B?
     
  4. Apr 14, 2012 #3

    Ray Vickson

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    Do you know the relationship between [itex] \det(A), \det(B) \text{ and } \det(AB)?[/itex]

    RGV
     
  5. Apr 14, 2012 #4
    Oh yes, it was incredibly simple: det(A)det(B)=det(AB) so det(A)det(B)=det(0) . I did one like this for symetric ones and I just didn't realize I could do the same here!
    Thank you guys!

    edit. What's RGV?
     
  6. Apr 14, 2012 #5

    Ray Vickson

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    It's a signature, the equivalent of "10-4 Good Buddy" or "over and out".

    RGV
     
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