That is, the element in the ith row and the jth column of C is obtained by multiplying the elements of the ith row of A by the corresponding elements of the jth column of B and summing over all terms; this is known as the row by column rule of multiplication. Thus, to obtain c 11, the element in the first row and the first column of C, we multiply the elements in the first row of A by the corresponding elements in the first column of B and sum over all terms. Similarly, to obtain c 12, we multiply the elements in the first row of A by the corresponding elements in the second column of B and sum over all terms, and so on.
Note that for multiplication to exist, matrices A and B must be conformable with respect to multiplication; that is, the number of columns in A must be equal to the number of rows in B. If, for example,
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