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anonymous

  • 4 years ago

I need to prove that if a and b are 3x3 diagonal matrices, than ab=ba. I have proved it, but I just made up two diagonal matrices and multiplied them together, to show that ab=ba. Is there a more mathematical way to prove this, or is this proof sufficient?

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  1. UnkleRhaukus
    • 4 years ago
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    if the matrices you used some how include all possible matrices then it has been proved, ie used matrices with letters for elements

  2. anonymous
    • 4 years ago
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    That is what I did. I got that both ab and ba =|dw:1328657180796:dw| so, that is enough proof?

  3. UnkleRhaukus
    • 4 years ago
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    sure

  4. phi
    • 4 years ago
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    looks ok. you could also use the fact that for diagonal matrix A \[ A^T = A \] and the general property \[ (AB)^T= B^TA^T=BA \]

  5. anonymous
    • 4 years ago
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    ah, so what your saying is that for any nxn matrix, ^^ hols true, and since 3x3 is an nxn, then that also holds true. Thanks!

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