anonymous
  • anonymous
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?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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UnkleRhaukus
  • UnkleRhaukus
if the matrices you used some how include all possible matrices then it has been proved, ie used matrices with letters for elements
anonymous
  • anonymous
That is what I did. I got that both ab and ba =|dw:1328657180796:dw| so, that is enough proof?
UnkleRhaukus
  • UnkleRhaukus
sure

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