Transformation Matrices represent the Location, Rotation and Scale of an object using a single concise 4x4 matrix, which is stored in the
matrix_world property of every object in Blender. Any transformation we do in space is handled under the hood through matrix multiplications with this matrix.
This is an interactive blend file that demonstrate how various transformations like Translation, Scaling and Rotation affect the Transformation Matrix of an object.
Play with the red cube's transformation and see for yourself how each transformation you do changes the Transformation Matrix.
Interactive blend file demonstrating how various transformations affect the Transformation Matrix of an object.