Suppose that one wants to have a group of matrices that satisfy some constraints. (As for a similar example, Pauli matrices satisfy some particular constraints.)
The constraint goes like following: (A matrix in the group is denoted $A_{ij}$; $ij$ is not referring to entries; it is used to label each matrix.
1) Matrices in the group commute.
2) For any matrix multiplication $B = A_{ij} \, A_{kl} \, A_{mn} \, ...$ if some particular number is used more than twice in $i,j,k,l,m,n,....$, the eigenvalue of $B$ becomes zero, and zero is the sole eigenvalue.
Can anyone provide me some hints?