  Starting from the expression for the superdeterminant of (xI-M), where M is
an arbitrary supermatrix, we propose a definition for the corresponding
characteristic polynomial and we prove that each supermatrix satisfies its
characteristic equation. Depending upon the factorization properties of the
basic polynomials whose ratio defines the above mentioned determinant we are
able to construct polynomials of lower degree which are also shown to be
annihilated by the supermatrix. Some particular cases and examples are
considered.
