# Precalculus : Find the Product of Two Matrices

## Example Questions

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### Example Question #65 : Matrices And Vectors

Calculate AB when

and .

Explanation:

In order to perform matrix multiplication, the number of columns in the first matrix has to be the same as the number of rows in the second column.

From here, we multiply each term in the first matrix's row by the first column in the second matrix. Continue in this fashion to get the product matrix.

### Example Question #66 : Matrices And Vectors

Evaluate:

Explanation:

Write the rule for multiplying a two by two matrix.  The result will be a two by two matrix.

Follow this rule for the given problem.

### Example Question #67 : Matrices And Vectors

Multiply the matrices:

Explanation:

In order to multiply these matrices we will need to consider the rows and columns for each matrix.

Both matrices have a dimension of .

The rule for multiplying matrices is where the number of columns of the first matrix must match the number of rows of the second matrix.

If the dimensions of the first matrix are , and the dimensions of the second matrix are , then we will get a dimension of  matrix as a result.  If the value of  are not matched, we cannot evaluate the product of the matrices.

### Example Question #68 : Matrices And Vectors

Find the product of A and B.

Explanation:

Since you are multiplying a  to a , the answer is going to be a .

To solve, simply multiply each corresponding element and add together.