Transpose Of A Matrix

We are given the equations involving matrix operations. First, solve for matrix and matrix from the given expressions.
1. From the first equation: Rearrange this equation to isolate : 2. From the second equation: Rearrange this equation to isolate : Now use the relationships derived above to find and , and finally calculate . Using the above relations and performing the calculations, we find that the final value of is: Thus, the correct answer is (D).

Given the matrix as: We are given the equation: We know that for any square matrix : Where is the determinant of matrix and is the identity matrix. First, calculate the determinant of matrix : Now, since the equation is , comparing both sides gives: Thus, the equation becomes: Simplifying: From this equation: Substitute this back into the expression : Now, equating the values: Thus, .