How Do You Multiply Matrices?

How Do You Multiply Matrices?

To multiply matrices, or arrays of numbers, multiply the like elements in each matrix. Before they can be multiplied, the two matrices have to have the same number of rows in one and columns in the other. If this is not the case, the matrices can't be multiplied. If you see a single number next to a matrix, it is a scalar and simply multiplies by each number in the matrix.

  1. Check the matrices for compatibility

    If the numbers of rows and columns in the opposite matrices do not match, the matrix product would be undefined. If they do match, proceed with multiplication.

  2. Multiply matching numbers

    As an example, assume the row of the matrix A includes the set [9 8 2] and the column of matrix B contains [4 2 3]. Multiply 9 by 4, 8 by 2 and 2 by 3.

  3. Add the products

    In the example, the first result comes to 36 + 16 + 6, or 58. Start a new matrix and place the number 58 in the top left position.

  4. Repeat as necessary

    Continue multiplying the rows and columns of matrix A and matrix B until all the spaces in the product matrix are filled.