71. (a) Let \( A=\left[\begin{array}{ccc}\sqrt{2} & 1 & 0 \\ 1 & -\sqrt{2} & 0 \\ 0 & 0 & \sqrt{3}\end{array}\right] \), then the value of \( \frac{\left|A^{-1}+A^{T}\right|}{|\operatorname{adj} \cdot(\operatorname{adj} \cdot A)|} \) is equal to
1) \( -\frac{2^{6} \sqrt{3}}{3^{8}} \)
2) \( \frac{2^{3}}{3^{6} \sqrt{3}} \)
3) \( -\frac{2^{9} \sqrt{3}}{3^{6}} \)
4) \( \frac{2^{3}}{3^{5}} \)
