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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