It is the purpose of this paper to make a study of commutation formulas in the algebra of quantum mechanics. The theories of quantum mechanics introduced by Heisenbergt and Diract are different in their conception and formulation but both make use of a non-commutative algebra. In Heisenberg's theory, the elements of the algebra are infinite matrices; in Dirac's they are abstract "q-numbers." Schrodinger's? theory, although mathematically equivalent to Heisenberg's, does not make explicit use of this algebra. However, the operators which Schrodinger uses satisfy the same commutation formulas as Heisenberg's matrices. We shall consider the algebra of the quantum mechanics from the matric standpoint although the results obtained do not depend upon the form of the variables. The variables enter in pairs as in classical mechanics and we shall use the expression "conjugate quantum variables" or simply "conjugate variables" in analogy with the idea of canonically conjugate variables in the classical theory. For a single pair of conjugate variables the properties of the algebra are determined by the fundamental commutation