GeoGebra Tutorial 22 – Spreadsheets, Vectors, and Matrices

This is the 22nd tutorial of the GeoGebra Intermediate Tutorial Series. If this is your first time to use GeoGebra, you might want to read the GeoGebra Essentials Series.

In this tutorial, we explore the relationship between the product of two 2 x 2 matrices. We set the entries of the factor matrices to integers, and limit the second matrix entries to values of -1, 0, and 1. We will also observe the relationship between their graphical interpretations.


First, we enter values of the first 2 x 2 matrix in cells A1, B1, A2 and B2, then create the multiplier matrix determined by sliders a, b, c and d. We enter the formulas of product matrix cells in E1, F1, E2 and F2. The ordered pairs (A1,B1), (A2,B2) are the factor matrix and the ordered pairs (E1,F1) and (E2,F2) will be the product matrix.

 You can view the output of this tutorial here. » Read more