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Suppose that there is a set of matrices.

1) $A^2 =0, C^2=0, E^2=0 .....$ and $AB+BA=0$, $CD+DC=0$... where $A,B,C..$ are matrices.

2) Matrices in the set either anticommute or commute.

3) $AD+BC \neq 0,... $

Is there any set of matrices that satisfies all of the aforementioned?

Edit: all matrices are not equal to each other.

  • 0
    3) seems to contradict 1) if required for *all* $A,D,B,C$ from the set.2012-10-27
  • 0
    @Berci how does it contradict? I am not gettting it.2012-10-27
  • 1
    Take $A=B=C=D$ and you have a contradiction.2012-10-27

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