SOLUTION: If A and B are matrices conformable for the product AB , prove that (AB)' = B'A'.

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Question 1077157: If A and B are matrices conformable for the product AB , prove that (AB)' = B'A'.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
(AB)'(AB) = I

(B'A')(AB) = [(B'A')A]B = [B'(A'A)]B = [B'I]B = B'B = I = (AB)'(AB)

So

(B'A')(AB) = (AB)'(AB)

Right multiply both sides by (AB)'

[(B'A')(AB)](AB)' = [(AB)'(AB)](AB)'

(B'A')[(AB)](AB)'] = (AB)'[(AB)(AB)']

(B'A')I = (AB)'I

B'A' = (AB)'

That's what we were to prove.

Edwin