What is Matrix Multiplication? Matrix multiplication is the process of multiplying two matrices together to get another matrix. It differs from scalar multiplication in that both things that you’re multiplying are matrices.

Requirements Say A and B are matrices. In order for us to be able to calculate A x B, the number of columns of A must equal the number of rows of B.

Multiplying Matrices When two matrices are multiplied together, the result is another matrix. When you multiply two matrices together, follow the “row by column” rule. To find the entry in row M and column N, multiply each entry in the Mth row of the first matrix by its corresponding entry in the Nth column of the second matrix and sum all of the results. To determine which entries correspond, count from left to right in the row and from top to bottom in the column.

Example

Implications We can infer several things about multiplying matrices from the row by column method. First, the first matrix must have as many columns as the second matrix has rows. This is so that the rows of the first matrix are the same length as the columns of the second matrix. Second, the final matrix will have as many rows as A does and as many columns as B does. Finally, matrix multiplication is not always commutative: A x B is not necessarily equal to B x A.

Example

Solution