- In the previous example, we can find the order of the answer matrix to be (2 x 2). Therefore, we know that there will be 4 elements as the final product.
- The 1st element in the answer matrix is found by multiplying the 1st row of the first matrix with the 1st column of the second matrix.
- The first element of the first row is multiplied by the first element of the first column.
- The second element of the first row is multiplied by the second element of the first column.
- Likewise, all the elements of the row are multiplied.
- Then the products of those are added and the first element of the answer matrix is found.
- This process is continued to find each element of the answer matrix.
Additional
- So to find the 2nd element of the answer matrix the 1st row of the first matrix is multiplied by the 2nd column of the second matrix.
- To find the 3rd element of the answer matrix the 2nd row of the first matrix is multiplied by the 1st column of the second matrix.
- To find the 4th element of the answer matrix the 2nd row of the first matrix is multiplied by the 2nd column of the second matrix.
\[\Large
A =
\begin{bmatrix}
product1 & product2\\
product3 & product4
\end{bmatrix}
\]
\[\Large A = \begin{bmatrix} AU + BW + CY & AV + BX + CZ \\ DU + EW + FY & DV + EX + FZ \end{bmatrix} \]
\[\Large A = \begin{bmatrix} AU + BW + CY & AV + BX + CZ \\ DU + EW + FY & DV + EX + FZ \end{bmatrix} \]