Multiplication of two matrices is possible if the number of columns in the

first matrix equals the number of rows in the second matrix.

Let ** A** be the first matrix and

*be the second matrix.*

**B**The dimensions of the first matrix *A *are , so the number of the columns

in the first matrix is 2.

The dimensions of the second matrix *B *are , so the number of the rows

in the second matrix *B *is 2.

The number of columns in the first matrix equals the number of rows in the

second matrix. So, matrix product is possible and its dimensions are .

Let P be the matrix product.

The matrix *P *is

The element of the matrix ()* *is the sum of the products

of the corresponding elements in the *i *^{th}* *row* *of the first matrix

()* *and column *j *^{th}* *column* *of the second matrix ().

where is the row index and .

Find the element .

The element is the sum of the products of the corresponding elements

of row 1 of the matrix A and column 1 of the second matrix..

Next find the element .

The element is the sum of the products of the corresponding elements

of row 1 of the matrix A and column 2 of the second matrix..

Next find the element .

The element is the sum of the products of the corresponding elements

of row 2 of the matrix A and column 1 of the second matrix.

Next find the element .

The element is the sum of the products of the corresponding elements

of row 2 of the matrix A and column 2 of the second matrix.

Simplify the product matrix.

The product matrix is .

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