# Pastebin uDgZDgDY
I whipped up this in raku:

  use Physics::Measure :ALL;

  sub infix:<·> { dot-product @^a, @^b }

  sub dot-product(@mx1, @mx2) {
    die "Incompatible dimensions for dot product."
        unless @mx1 == @mx2[0] && @mx1[0] == @mx2;

    [for ^@mx1 -> $i {
        [for ^@mx1 -> $j {
            [+] @mx1[$i;*] >>*<< @mx2[*;$j]
        }]  
    }]  
  }

  my @m = [[1m,2m],[3m,4m]]; 

  say @m · [Z] @m;    #[[5m^2 11m^2] [11m^2 25m^2]]

Since Physics::Measure is strong on illegal combinations and since there are not many realistic random combinations of Units (s^2 anyone) I have not gone random for my example.