# Matrix Multiplication

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Matrix multiplication is not straight-forward and an important thing to remember is that it is non-commutative (i.e. $AB{\ne}BA$ )

To multiply two matrices together you sort of multiply rows by columns. However, in order to multiply two matrices together, the matrix being post-multiplied must have the same number of columns as the matrix being pre-multiplied has rows (e.g. you cannot post-multiply a 3x2 matrix by a 3x4 matrix, but you can post-multiply a 2x3 matrix by a 3x4 matrix: the result will be a 2x4 matrix).

In general...

$\left[\begin{matrix}a_1&a_2&a_3\\b_1&b_2&b_3\end{matrix}\right]\left[\begin{matrix}c_1&c_2\\d_1&d_2\\e_1&e_2\end{matrix}\right]=\left[\begin{matrix}a_1c_1+a_2d_1+a_3e_1&a_1c_2+a_2d_2+a_3e_2\\b_1c_1+b_2d_1+b_3e_1&b_1c_2+b_2d_2+b_3e_2\end{matrix}\right]$

See http://mathworld.wolfram.com/MatrixMultiplication.html for more information
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