How to place a vertical dashed line between columns of a matrix?

I will add another simple solution if you like.

documentclass{article}
usepackage{arydshln}
usepackage{mathtools}
begin{document}
[ left[
begin{array}{c:c}
1 &  2 \ 
3 & 4 \
5 & 6 \ 
end{array} right] ]
end{document}

ADDENDUM: 2020-7-24. Using {bNiceArray} of nicematrix package you will have the square brackets at the same position as in {bmatrix} of amsmath.

documentclass[a4paper,12pt]{article}

usepackage{nicematrix}
usepackage{arydshln}

NiceMatrixOptions{letter-for-dotted-lines=V}

begin{document}
$begin{bNiceArray}{c:c}
1 & 2 \
3 & 4 \
5 & 6
end{bNiceArray}$
end{document}

Remark: If you don't put NiceMatrixOptions{letter-for-dotted-lines=V}, you will have a dotted line (drawn by nicematrix).

Try

documentclass{article}
usepackage{amsmath}
usepackage{arydshln}
begin{document}
begin{equation}
left[
    begin{array}{c;{2pt/2pt}c}
        -2 & -4 \
         2 & -1 \
        -8 & 16
    end{array}
right]
end{equation}
end{document}

To obtain