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?

Question

unklerhaukus · Answer

if the matrices you used some how include all possible matrices then it has been proved,
ie used matrices with letters for elements

anonymous · Answer

That is what I did. I got that both ab and ba =|dw:1328657180796:dw|  so, that is enough proof?