On $k$-commutative matrices

The matrices Bi, defined by these relations, have significance in the study of the Lie groups of infinitesimal rotations and have been studied by numerous writers. Particular attention is invited to the references I-XVIIJ.t In the present paper we shall study the commutes of a pair of matrices as a part of matric algebra and shall not attempt to interpret the significance the results may have in modern physical theories.