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Matrix Multiplication

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In general for, any matrix multiplication, the ith row and jth column of the product matrix is the dot product of the ith row of the first matrix and the jth column of the second matrix.

For example, for two 2x2 matrices, the product matrix is:

$$ \begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} w & x \\ y & z \end{pmatrix} = \begin{pmatrix} aw + by & ax + bz \\ cw + dy & cx + dz \end{pmatrix}$$

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