Matrix MultiplicationYou are currentlybrowsing as guest. Click here to log in 

Matrix multiplication is not straightforward and an important thing to remember is that it is noncommutative (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 postmultiplied must have the same number of columns as the matrix being premultiplied has rows (e.g. you cannot postmultiply a 3x2 matrix by a 3x4 matrix, but you can postmultiply a 2x3 matrix by a 3x4 matrix: the result will be a 2x4 matrix).
In general...
$\left[\begin{matrix}a_1&a_2&a_3\\b_1&b_2&b_3\end{matrix}\right]\left[\begin{matrix}c_1&c_2\\d_1&d_2\\e_1&e_2\end{matrix}\right]=\left[\begin{matrix}a_1c_1+a_2d_1+a_3e_1&a_1c_2+a_2d_2+a_3e_2\\b_1c_1+b_2d_1+b_3e_1&b_1c_2+b_2d_2+b_3e_2\end{matrix}\right]$
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