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Step-by-step Answer
PAGE: 212SET: ExercisesPROBLEM: 1
Please look in your text book for this problem Statement

The matrices are .

If A and B are inverse then .

The dimension of the two matrices is

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.

Since  , they are not inverse .

The two matrices are not inverse .



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