# Calculating the number of operations in matrix multiplication

Is there a formula to calculate the number of multiplications that take place when multiplying 2 matrices? For example

$$\begin{pmatrix}1&2\\3&4\end{pmatrix} \times \begin{pmatrix}5&6\\7&8\end{pmatrix} = \text{8 multiplications and 4 additions}$$

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## migrated from mathoverflow.netSep 5 '13 at 6:51

This question came from our site for professional mathematicians.

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