A transformation matrix is a mathematical tool used in geometry to perform operations like rotation, scaling, and translation on objects in space. By representing these operations in matrix form, we can easily manipulate coordinates of points or shapes. For example, if you want to rotate a square around its center, you can use a transformation matrix to calculate the new positions of its corners. These matrices are especially useful in computer graphics, where they help create realistic animations and visual effects. By applying a series of transformation matrices, artists can move, resize, or change the orientation of objects, making it easier to design complex scenes in software like Adobe Photoshop or Blender.