Question

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?

Answer 1

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

Answer 2

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