(a) Let \( A=\left[\begin{array}{ccc}\sqrt{2} & 1 & 0 \\ 1 & -\sqrt{2} & 0 \\ 0 & 0 & \sqrt{3}\end{array

(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 \( \frac{\left|A^{-1}+A^{T}\right|}{|\operatorname{adj} .(\operatorname{adj} . A)|} \) is equal to

(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 \( \frac{\left|A^{-1}+A^{T}\right|}{|\operatorname{adj} .(\operatorname{adj} . A)|} \) is equal to

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