$\"\"$ Multiplication of two matrices is possible if the number of columns in the first matrix equals the number of rows in the second matrix.

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Let A be the first matrix and B be the second matrix.

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The dimensions of the first matrix A are $\"\"$ , so the number of the columns in the first matrix is 2.

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The dimensions of the second matrix B are $\"\"$ , so the number of the rows in the second matrix B is 2. $\"\"$

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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 $\"\"$ .

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Let P be the matrix product.

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$\"\"$

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The matrix P is

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$\"\"$ $\"\"$ 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 ( $\"\"$ ).

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$\"\"$ where $\"\"$ is the row index and $\"\"$ .

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$\"\"$ Find the element $\"\"$ .

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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.

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$\"\"$ .

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$\"\"$ $\"\"$ Next find the element $\"\"$ .

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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.

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$\"\"$ .

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$\"\"$ $\"\"$ Next find the element $\"\"$ .

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The element $\"\"$ is the sum of the products of the corresponding elements of row 1 of the matrix A and column 3 of the second matrix.

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$\"\"$ .

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$\"\"$ $\"\"$ Next find the element $\"\"$ .

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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.

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$\"\"$ .

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$\"\"$ $\"\"$ Next find the element $\"\"$ .

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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.

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$\"\"$ .

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$\"\"$ $\"\"$ Next find the element $\"\"$ .

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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.

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$\"\"$ .

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$\"\"$ $\"\"$ Next find the element $\"\"$ .

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The element $\"\"$ is the sum of the products of the corresponding elements of row 3 of the matrix A and column 1 of the second matrix.

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$\"\"$ .

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$\"\"$ $\"\"$

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Next find the element $\"\"$ .

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The element $\"\"$ is the sum of the products of the corresponding elements of row 3 of the matrix A and column 2 of the second matrix.

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$\"\"$ .

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$\"\"$ $\"\"$

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Next find the element $\"\"$ .

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The element $\"\"$ is the sum of the products of the corresponding elements of row 3 of the matrix A and column 3 of the second matrix.

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$\"\"$ .

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$\"\"$ $\"\"$

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Simplify the product matrix.

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$\"\"$ $\"\"$

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The product matrix is $\"\"$