The commutator of two operators A and B, which measures the degree of incompatibility between A and B, is AB - BA (at least according to one textbook I have). But multiplying/substracting matrices just yields matrices! (http://en.wikipedia.org/wiki/Matrix_multiplication). So firstly, how can a matrix measure incompatibility? Secondly, how can this equation be valid if the commutator of position and momentum is a number i times h-bar? Thirdly, how is a weird number like i times h-bar a measure of anything? Very confused, please help.