The same question which I asked previously. But I did different solution from the previous one. I solved this by using given hint.
Previous question and solution are this: Question on maximum likelihood estimation
Question:
My new answer is as follows:
Please check my solution. I am really not sure about this solution. And please tell me my mistakes and missing. Thanks a lot!
Seems right, just note that $X$ is not a square matrix, hence $$ (X'X)^{-1}\neq X^{-1}(X')^{-1}, $$ however you result still holds as $$ tr(X(X'X)^{-1}X')=tr(X'X(X'X)^{-1})=tr(I_k)=k. $$