Then ive misunderstood my professor.
he can prove that if F is a field, Char(F)=0, A matrix = Â Mnxm(F), B matrix = Â Mmxn(F),
AB=In
And
BA=Im
Then A is  a square matrix.
his way: at the beggining he proved that if A matrix = Mnxm(F), B matrix = Mmxn(F) then tr(AB)=tr(BA).
then he said n=tr(In)=tr(AB)=tr(BA)=tr(Im)=m then n=m
BUT HE DIDNT EVEN USE THE FACT CHAR(F)=0 AND HE SAID ITS HARD TO PROVE IT WITHOUT HAVING THE FACT CHAR(F)=0. I KNOW I MISUNDERSTOOD HIM BUT MY QUESTION IS WHERE. ITS FREAKING ME OUT.
by the way, what are you doing nowadays? are you a professor or something?
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sorry i resent it because something fucked up for some reason