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## Matrix Multiplication

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.

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