Let $M,N$ be $n\times n$ matrices. Then why is it that $MN-NM=I_n$ cannot be true, where $I_n$ is the $n\times n$ identity matrix?
I am thinking of perhaps there is an argument using determinants? (Of course I am probably way out.)
Thanks.
Let $M,N$ be $n\times n$ matrices. Then why is it that $MN-NM=I_n$ cannot be true, where $I_n$ is the $n\times n$ identity matrix?
I am thinking of perhaps there is an argument using determinants? (Of course I am probably way out.)
Thanks.
Thanks to @t.b.,
$\operatorname{tr}(AB-BA)=\operatorname{tr}(I) \implies \operatorname{tr}(AB)-\operatorname{tr}(AB)=n$
Contradiction.