Teaching the noncommutativity of the product of matrices to high school or college level students is a difficult task when approached from a purely formal perspective. The aim of this paper is to present a simple experimental activity for teaching the noncommutativity of the matrix product, based on the Jones calculus, a mathematical formalism for describing polarised light by means of matrices and vectors. This activity can also be useful to introduce students to the use of matrices in physics, and to illustrate how abstract mathematics can become a powerful tool to help us explain and describe the real world.