it is known that a square matrix A may commute with B, and that the same matrix A may commute with C, but B and C do not commute. This is true only if all the matrices are derogatory, see for example:
My question is the following: which may be a procedure to generate the matrices A, B, and C which are so non-diagonalisables and have the shown property ? If some body may give me some tips or indicate a bibliographical reference, it will be fine.
Thanks in advance