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

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