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True or false, about determinant (linear algebra)

  1. Jan 26, 2009 #1

    fluidistic

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    Gold Member

    1. The problem statement, all variables and given/known data
    If det (AB)=0 then A or B doesn't have an inverse. True or false?

    2. The attempt at a solution
    As det (AB)= det(A)*det(B)=0, it's clear that or det(A)=0, or det(B)=0 or both are worth 0. Meaning that there is at least A or B not inversible.
    But this is only true when A and B are square matrices. Because I don't think the inverse of a matrix has sense when we are talking about nxm matrices, with m different from n.
    Am I right? So my answer is FALSE.
     
  2. jcsd
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