For the given orthogonal matrix Q
\[{\text{Q}} = \left[ {\begin{array}{*{20}{c}} {\frac{3}{7}}&{\frac{2}{7}}&{\frac{6}{7}} \\ { - \frac{6}{7}}&{\frac{3}{7}}&{\frac{2}{7}} \\ {\frac{2}{7}}&{\frac{6}{7}}&{ - \frac{3}{7}} \end{array}} \right]\]
The inverse is

A. \[\left[ {\begin{array}{*{20}{c}} {\frac{3}{7}}&{\frac{2}{7}}&{\frac{6}{7}} \\ { - \frac{6}{7}}&{\frac{3}{7}}&{\frac{2}{7}} \\ {\frac{2}{7}}&{\frac{6}{7}}&{ - \frac{3}{7}} \end{array}} \right]\]

B. \[\left[ {\begin{array}{*{20}{c}} { - \frac{3}{7}}&{ - \frac{2}{7}}&{ - \frac{6}{7}} \\ {\frac{6}{7}}&{ - \frac{3}{7}}&{ - \frac{2}{7}} \\ { - \frac{2}{7}}&{ - \frac{6}{7}}&{\frac{3}{7}} \end{array}} \right]\]

C. \[\left[ {\begin{array}{*{20}{c}} {\frac{3}{7}}&{ - \frac{6}{7}}&{\frac{2}{7}} \\ {\frac{2}{7}}&{\frac{3}{7}}&{\frac{6}{7}} \\ {\frac{6}{7}}&{\frac{2}{7}}&{ - \frac{3}{7}} \end{array}} \right]\]

D. \[\left[ {\begin{array}{*{20}{c}} { - \frac{3}{7}}&{\frac{6}{7}}&{ - \frac{2}{7}} \\ { - \frac{2}{7}}&{ - \frac{3}{7}}&{ - \frac{6}{7}} \\ { - \frac{6}{7}}&{ - \frac{2}{7}}&{\frac{3}{7}} \end{array}} \right]\]

Answer: Option C