Question

If \( A = \frac{1}{3} \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b \end{bmatrix} \) is an orthogonal matrix, then

• A. \( a = -2, b = -1 \)
• B. \( a = 2, b = 1 \)
• C. \( a = 2, b = -1 \)
• D. \( a = -2, b = 1 \)

Hint:

Remember that for an orthogonal matrix \( A \), \( AA^T = I \).