From Math Images
A transformation matrix is a special matrix that can describe transformations.
Transformation matrices can represent two dimensional transformations as well as three dimensional transformations. Each type of transformation is represented by certain elements in the matrix.
Examples in 2D Graphics
In 2D graphics Linear transformations can be represented by 2x2 matrices. Most common transformations such as rotation, scaling, shearing, and reflection are linear transformations and can be represented in the 2x2 matrix. Other affine transformations can be represented in a 3x3 matrix.