# counting functions.

let f be a linear functional on M(n,F) , vector spaces of n x n matrices over F(field) satisfying following properties. (i) f(AB) = f(BA) ; for all A,B belongs to M(n,F). (II)f(I) = n ; for I the identity matrix of order n x n. let S be the set of all such functionals on M(n,F) satisfying all these properties (i) and (ii). |S|= number of element of S