$\"\"$

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The matrices are $\"\"$ .

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If A and B are inverse then $\"\"$ .

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The dimension of the two matrices is $\"\"$ $\"\"$

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

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

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The element $\"\"$ of the matrix ( $\"\"$ ) is the sum of the products

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of the corresponding elements in the i ^th row of the

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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

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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

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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

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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

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

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$\"\"$ . $\"\"$ $\"\"$ Simplify the product matrix.

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$\"\"$

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Since $\"\"$ , they are not inverse .

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$\"\"$ The two matrices are not inverse .