Two 3 × 3 transformation matrices can similarly be multiplied to produce the transformation matrix that described the net result of applying one of the original two transformations followed by the other.

For example, suppose we first perform the transformation described by

and then perform the transformation described by

The matrix that describes the transformation from all the way to is computed by multiplying the matrices associated with the individual transformations. The rules of multiplication generalize for 3 × 3 matrices such that

Practice
Matrix Multiplication

Try out multiplying some sample 3 × 3 transformation matrices.