2D Matrix Transformations on a Square

This GeoGebra example dynamically demonstrates how a square undergoes various 2D matrix transformations such as rotation, scaling, and shearing. The core mathematical concept is linear transformation and matrix multiplication, showing the relationship between basis vectors (e₁, e₂) and their images (e₁', e₂'), and how the transformation matrix M acts on points like A, B, P1, and P2. The construction uses the ApplyMatrix command to map the square's vertices, while also displaying the basis vectors and their transformed counterparts to reveal the geometric meaning of matrix columns. Sliders or input fields allow real-time adjustment of matrix entries, with auxiliary objects like text labels (text1, text2, text3) and images (pic1) enhancing visualization. Suitable for high school or early college students learning linear algebra, analytic geometry, or computer graphics fundamentals, and for teachers demonstrating the geometric interpretation of matrix transformations in class.