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Interesting Matrix Question

  1. Oct 8, 2004 #1
    Are there two matrices A and B such that A*B is the zero matrix but B*A is not?

    I'm leaning toward no.. I'm composing my solution right now.

    Bah the only thing I can come up with is that if any row of A can be treated as a vector and any column of row B can be treated as a vector, for element (i, j) in the matrix AB will be 0 iff the vector of row i in A and column j in B are orthogonal (dot product is 0). I can't get much further right now :(
     
    Last edited by a moderator: Oct 8, 2004
  2. jcsd
  3. Oct 8, 2004 #2
    A=
    [tex]
    \left\{
    \begin{array}{ccc}
    1 & 1 \\
    0 & 0
    \end{array}
    \right\}
    [/tex]

    B=
    [tex]
    \left\{
    \begin{array}{ccc}
    1 & 1 \\
    -1 & -1
    \end{array}
    \right\}
    [/tex]

    -- AI
     
  4. Oct 8, 2004 #3
    Thanks. Although the question did just originally ask what is an example after many hours of scratching my head I made a proof that would satisfy that. Thank you for a template to go by though it facilitated the process a little.
     
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