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is there any set of matrices, numbers or objects that satisfy the following?

1) $AB=0$ where A and B are different objects inside the set

2) they commute.

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    Sure. $$\begin{pmatrix} 0 & 0 \\ 0 & 1 \end{pmatrix}\begin{pmatrix}1 & 0 \\ 0 & 0\end{pmatrix}= \begin{pmatrix}1 & 0 \\ 0 & 0\end{pmatrix}\begin{pmatrix} 0 & 0 \\ 0 & 1 \end{pmatrix} = \begin{pmatrix}0 & 0 \\ 0 & 0 \end{pmatrix}$$ Did you have additional constraints in mind?2012-10-27

2 Answers 2