Dirac matrices as elements of a superalgebraic matrix algebra

A Clifford extension of the Grassmann algebra is considered in which operators are built from products of Grassmann variables and derivatives with respect to them. It is shown that a subalgebra of operators, isomorphic to the usual matrix algebra, can be separated in this algebra, while the algebra itself is a generalization of the matrix algebra, contains superalgebraic operators expanding the matrix algebra, and produces transformations of supersymmetry.