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:

Orthogonal matrices have mutually orthogonal rows of unit length.

Answer 1

The Correct Option is C