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 B be the second matrix.

The dimensions of the first matrix A are , so the number of the

columns in the first matrix is 1.

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

rows in the second matrix B is 1.

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 1 of the matrix A and column3 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.

.

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 3 of the second matrix.

.

Simplify the product matrix.

The product matrix is