I need to prove that if A and B are matrices such AB and BA exist, and AB is symmetric (so AB = (AB)transpose ), show that AB=Ba.
So far I can prove that AB and BA have the same size, but I can't figure out how to prove that they have the same entries.
Proof of size:
A is m*n, B is n*p. So AB is m*p, but since BA exists too m must = p. So now A is m*n, and B is n*m. This leads to AB being m*m and BA being n*n. And since AB=BA m must = n so all of the mentioned matrices must be n*n in size.
now i just need to prove that the entries of AB and BA are the same.
2006-08-10
19:39:33
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4 answers
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asked by
darcy_t2e
3
in
Mathematics