% example from list by xan

\definemathmatrix
  [det]
  [left={\left\lvert\,},
   right={\,\right\rvert},
   strut=1.25]

\setupwhitespace[big]

\starttext

$\startdet[n=3]
    \NC yz \NC \ruledhbox{$\frac{1}{x}$} \NC x \NR
    \NC yz \NC \ruledhbox{$\frac{1}{x}$} \NC x \NR
    \NC yz \NC \frac{1}{x} \NC x \NR
    \NC zx \NC \frac{1}{y} \NC y \NR
    \NC xy \NC \frac{1}{z} \NC z \NR
\stopdet$

Whatever:

\startitemize[a,columns]

    \startitem $\startdet[n=4]
        \NC 1 \NC 1 \NC  1 \NC  1 \NR
        \NC 1 \NC 2 \NC  3 \NC  4 \NR
        \NC 1 \NC 3 \NC  6 \NC 10 \NR
        \NC 1 \NC 4 \NC 10 \NC 20 \NR
    \stopdet$ \stopitem

    \startitem $\startdet[n=4]
        \NC 1 \NC -2 \NC  0 \NC  1 \NR
        \NC 1 \NC  1 \NC  0 \NC  2 \NR
        \NC 0 \NC  3 \NC -2 \NC -1 \NR
        \NC 1 \NC  1 \NC  1 \NC  3 \NR
    \stopdet$ \stopitem

    \startitem $\startdet[n=5]
        \NC 1 \NC 2 \NC 3 \NC 4 \NC 5 \NR
        \NC 2 \NC 3 \NC 4 \NC 5 \NC 1 \NR
        \NC 3 \NC 4 \NC 5 \NC 1 \NC 2 \NR
        \NC 4 \NC 5 \NC 1 \NC 2 \NC 3 \NR
        \NC 5 \NC 1 \NC 2 \NC 3 \NC 4 \NR
    \stopdet$ \stopitem

    \startitem $\startdet[n=3]
        \NC 1 \NC 2 \NC  3 \NR
        \NC 1 \NC 4 \NC  9 \NR
        \NC 1 \NC 8 \NC 27 \NR
    \stopdet$ \stopitem

\stopitemize

And more:

\startitemize[a]

    \startitem $\startdet[n=3]
        \NC -\sqrt{3} \NC 3                \NR
        \NC 5         \NC -\sqrt{3}\cdot 5 \NR
    \stopdet$ \stopitem

    \startitem $\startdet[n=3]
        \NC  2 \NC 1 \NC  3 \NR
        \NC  1 \NC 0 \NC  1 \NR
        \NC -3 \NC 2 \NC -1 \NR
    \stopdet$ \stopitem

\stopitemize

$\startdet[n=3]
    \NC yz \NC \ruledhbox{$\frac{1}{x}$} \NC x \NR
    \NC yz \NC \ruledhbox{$\frac{1}{x}$} \NC x \NR
    \NC yz \NC \frac{1}{x}               \NC x \NR
    \NC zx \NC \frac{1}{y}               \NC y \NR
    \NC xy \NC \frac{1}{z}               \NC z \NR
\stopdet$

\stoptext
