The preceding section looked at multiplying a scalar and a matrix. The next logical step is to investigate the product of two matrices, or a matrix times another matrix. This process involves the dot product, so you might want to flip back to Chapter 4, “Vector Operations,” for a quick review of the dot product before proceeding.
You can multiply matrices by taking a series of dot products. Keep in mind two important aspects of the dot product:
The two vectors must have the same number of entries to take the dot product.
The dot product returns a scalar quantity (a single number).
Let's start by looking at two 2×2 matrices. Matrices to be multiplied don't have to be square and don't have to be the same size, but there are ...