A Discovery lesson on Matrix Inverses
In the Madison Project text Explorations in Mathematics there are several chapters dealing with the system of 2 × 2 matrices. 1 When investigating some of these chapters with fifth or sixth graders, I have always been amazed to see how quickly they can figure out the identity matrix for multiplication; on the other hand, it seems very difficult for these students to figure out the inverse of a 2 × 2 matrix. The technique proposed in the text of just presenting two matrices whose product is the identity seems too arbitrary for my pedagogical taste, so I have preferred to go through another procedure of looking for the inverse to particular matrices and then trying to find relationships between the elements of the two matrices.