Word Count : 313

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To prove that the given matrix is orthogonal, we need to show that: \[ A^T A = I \] where \( A^T \) is the transpose of matrix \( A \) and \( I \) is the identity matrix. ### Step 1: Given Matrix The given matrix is: \[ A = \begin{bmatrix} \cos 2\alpha & -\sin 2\alpha \\ \sin 2\alpha & \cos 2\alpha \end{bmatrix} \] ### Step 2: Compute the Transpose of \( A \) The transpose of _____ _______ _____ _____ _____ ______ ___ __________ ____ ___ __________.
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