I tried to write it all out, but it becomes really messy... Is there a more elegant way to do it?
Note that I don't know about dimensions, vector spaces & bases yet
2026-03-26 22:27:16.1774564036
Show that if $A,B$ are $2\times2$ matrices, then $(AB-BA)^2$ commutes with all $2\times2$ matrices.
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$AB-BA$ has trace zero, so has the form $\pmatrix{u&v\\w&-u}$. What happens when you square such a matrix?