Non-commutative refers to a property in mathematics and physics where the order of operations affects the outcome. In simpler terms, if you change the sequence of two elements, the result may differ. For example, in the case of matrix multiplication, multiplying matrix A by matrix B does not yield the same result as multiplying B by A. This concept is crucial in various fields, including quantum mechanics, where the non-commutative nature of certain operators leads to fundamental principles like the uncertainty principle. Understanding non-commutativity helps in grasping complex systems and behaviors in both mathematics and science.