Table of Contents## Matrix Multiplication

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You may be thinking that matrix multiplication works in a
similar manner, and that’s how you can do a `scale()`

transformation. Unfortunately, the
easy way doesn’t work this time. Matrix multiplication is significantly
more complicated than matrix addition. In the first examples that
follow, this complexity appears to be needless. As we proceed, you’ll
see that the usefulness of matrix multiplication far outweighs its
difficulty.

In order to multiply two matrices, the number of
*columns* of the first matrix must equal the number
of *rows* of the second matrix. Such matrices are
called compatible. This means you can multiply a 3-by-5 matrix times a
5-by-4 matrix, but not a 3-by-5 matrix times a 3-by-2 matrix. The
matrices we will multiply in Figure
D-5 are compatible.