  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.
