I heard somewhere that $AB=0$ is related to $A^2+B^2$.
So, does $AB=0$ result in $A^2+B^2 =0$?
Or if it doesn't, which matrices would satisfy $AB=0$ while $A^2+B^2=0$
Edit: right. stupid me. So, let me add the following condition:
Suppose $AB=0, CD=0, EF=0....$ and $A^2+B^2=0, C^2+D^2=0, E^2+F^2=0....$. Except zero matrix, is there any case when a set of matrices have the aforementioned property?