Geometric Visualization of Matrix Multiplication

This example visualizes how multiplying two matrices corresponds to composing two linear transformations acting on geometric objects. It helps learners see that the product A·B can be interpreted as “apply B first, then apply A” by comparing transformed shapes side by side. The key mathematical ideas are matrix multiplication, linear transformation of coordinates, and vertex/point mapping to polygons so that the resulting configuration reflects the algebraic operation. Construction-wise, it uses GeoGebra commands including Random to generate representative data, LaTeX to display matrix or formula text, and Polygon to create and update polygon geometries (e.g., poly1, poly2, poly4). Multiple point sets (labeled a–h and A–O, plus derived points like c_2, d_1, e_1, f_1, g_1, h_1, etc.) are used to build the pre- and post-transformation vertices, with annotations (text1/text2) to support the comparison. Suitable for high school to early college audiences studying introductory linear algebra and for classroom demonstrations or interactive exploration.