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If $(AB)'=B'A'$ then $(x'x)^{-1}x'$ should be equal to $x((x'x)^{-1})'$ . However most econometrics textbooks say that this is equal to $x(x'x)^{-1}$ . What happened to the transpose of $(x'x)^{-1}$? According to the rule it should have a transpose.

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  • $\begingroup$ What does ' mean here? $\endgroup$ – Cameron Williams Feb 2 '14 at 2:29
  • $\begingroup$ @CameronWilliams: I think ' means transpose $\endgroup$ – voldemort Feb 2 '14 at 2:31
  • $\begingroup$ Yes, it means transpose. $\endgroup$ – Sophie Feb 2 '14 at 2:38
  • $\begingroup$ What is the source of this question, is it from a book? Since you're new, my advice is maybe you can clarify your question to avoid getting down voted so much. $\endgroup$ – grayQuant Feb 2 '14 at 6:15
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Let $a=x'x$ and $b=a^{-1}$. Then $a'=(x'x)'=x'x''=x'x=a$ hence $b'=b$. Thus your suggestion to use the transpose of $(x'x)^{-1}$ and the practice of using $(x'x)^{-1}$ instead, are in fact equivalent.

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