# How to Multiply Matrices

Multiplying matrices is painless when you understand the method described here.

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#### You Will Need

• Compatible matrices
• Calculator

## Steps

1. Step 1

#### Check rows and columns

Makes sure the number of columns in the first matrix equals the number of rows in the second.

2. Unless the number of columns in the first matrix equals the number of rows in the second, their product will be undefined.

3. Step 2

#### Calculate the (row 1, column 1) entry

Place the sum of the products from row 1 of the first matrix and column 1 of the second matrix in the (row 1, column 1) position of the product matrix.

4. Step 3

#### Calculate the (row 2, column 1) entry

Place the sum of the products from row 2 of the first matrix and column 1 of the second matrix in the (row 2, column 1) position of the product matrix.

5. Step 4

#### Calculate the remaining entries

Continue multiplying the elements of the rows of the first matrix by the elements of the columns in the second matrix until you have formed a product matrix with the dimensions of (rows of the first matrix) by (columns of the second matrix).

6. The word matrix comes from the Latin word for mother.