Transpose Of A Matrix

We are given the matrix and we need to find its inverse.

Step 1: First, calculate the determinant of matrix .

Step 2: Now, calculate the adjoint of matrix . The adjoint is the transpose of the cofactor matrix.

Step 3: Using the formula for the inverse of a matrix , we find:

Conclusion: The correct inverse matrix is:

We are given that is the adjoint of a matrix and the determinant of , . The adjoint is related to the determinant of as follows: The elements of are cofactors of the corresponding elements in , so the element (second element in the first row) is the cofactor of , which is . The cofactor is equal to multiplied by the corresponding minor of . From the question, we are told that . For , we can compute the cofactor corresponding to the matrix element. The matrix suggests that for , the cofactor corresponding to (which is ) is 1.
Conclusion: Therefore, .