Is there a set of matrices that satisfy all of the following constraints?
1) $A^2=0, B^2=0, C^2=0...$ where $A,B,C,D..$ are different matrices.
2) All of them commute.
Edit: 3) $AB \neq 0, AC \neq 0, BC \neq 0, ...$.
Is there a set of matrices that satisfy all of the following constraints?
1) $A^2=0, B^2=0, C^2=0...$ where $A,B,C,D..$ are different matrices.
2) All of them commute.
Edit: 3) $AB \neq 0, AC \neq 0, BC \neq 0, ...$.