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When is matrix multiplication commutative

  1. Sep 15, 2009 #1
    Can somebody please explain to me when matrices commute? I've read that it's when they are diagonal with the same dimensions (and also scalar multiples?), but I don't understand why this is.
     
  2. jcsd
  3. Sep 15, 2009 #2

    HallsofIvy

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    Well, for example, what is
    [tex]\begin{bmatrix}a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c\end{bmatrix}\begin{bmatrix}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{bmatrix}[/tex]
    and what is
    [tex]\begin{bmatrix}x & 0 & 0 \\ 0 & y & 0 \\ 0 & 0 & z\end{bmatrix}\begin{bmatrix}a & 0 & 0 \\ 0 & b & 0 \\ 0 & 0 & c\end{bmatrix}[/tex]

    If you can see why those are the same, you should be able to generalize to any dimension.
     
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