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...


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