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Provided both matrices are mutable, two matrices A and B can be swapped like any other two items: create temporary storage to store a copy of A, then assign B to A, and finally assign the temporary copy of the previous version of A to B.

Note that in the C Programming language, matrices cannot be assigned to each as such. One implementation of this algorithm might operate on the basis of references (pointers), and can thus swap two matrix references by swapping two pointers in the manner detailed above. Implementations wishing to actually transfer the data held in one matrix to another would use a library function such as memcpy() to transfer data.

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