Solution
= Solution
Let $N=\sqrt8\,A$ be the unscaled <matrix>. Expansion along its third row gives
$$
\det N=2(\sqrt2+\sqrt{18})+2(\sqrt{18}+\sqrt2)=16\sqrt2.
$$
Scaling a three-by-three <matrix> by $1/\sqrt8$ scales its <determinant> by $(\sqrt8)^{-3}$. Therefore
$$
\boxed{\det A=\frac{16\sqrt2}{(\sqrt8)^3}=1}.
$$