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the number of columns of A must equal the number of rows of B in order to get the product matrix AB.
The final product will have
as many rows as A and as many columns as B.
Recall that the final product will have as many rows as the first matrix and as many columns as the second matrix. Be sure to write the dimensions in the form number of rowsnumber of columns.
First simplify the matrices in the parentheses, then find the resulting product. The product AB of two matrices A and B can be found only if the number of columns in A is the same as the number of rows in B. Let A be an mn matrix and let B be an nk matrix. To find the element in the ith row and jth column of the product matrix AB, multiply each element in the ith row of A by the corresponding element in the jth column of B, and then add these products. The product AB is an mk matrix.
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