Question

For some \( a \leq 0 \) and \( b \in \mathbb{R} \), let
\[A = \begin{pmatrix} 0 & a & b \\ -\frac{1}{\sqrt{2}} & \frac{1}{\sqrt{6}} & \frac{1}{\sqrt{3}} \\ \frac{1}{\sqrt{2}} & \frac{1}{\sqrt{6}} & \frac{1}{\sqrt{3}} \end{pmatrix}.\]
If \( A \) is an orthogonal matrix, then the value of \( a\sqrt{6} + 4b\sqrt{3} \) is equal to __________ (answer in integer).

Answer 1

Correct Answer: 2

The correct Answer is : 2-2(Approx.)