If $AB+BA=0$, then $A^2B^3=B^2A^3$? If I have a matrix $A$ and $B$ such that $AB+BA=0$
is it true that $A^2B^3=B^2A^3$?
I think that it is false.

Similarly to O.L.'s answer, we have the quaternions $ij+ji=k-k=0$, but $i^2j^3=j$ and $j^2i^3=i$.
