Matrix Algebra

Step 1: Compute the transpose of matrix . The transpose of , denoted as , is obtained by swapping the off-diagonal elements: Step 2: Add and . Adding corresponding elements: Simplifying: Step 3: Equating to the identity matrix. The identity matrix is: Thus, equating: From which: Step 4: Finding . Using the Pythagorean identity: Substituting : Conclusion: The correct answer is .

Step 1: Begin by calculating . Multiply the matrix by itself: Perform the matrix multiplication : Step 2: Carry out the multiplication: Simplifying: Step 3: Now, compute , where is the identity matrix: Thus: This is equal to .