This:

 for ($a=0; $a<=$#columns; $a++) {
      for ($b=0; $b<=$#columns; $b++) {
        print "$list[$a][$b] "; # for testing
      }
      print " \n";
   }
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should probably avoid using the $a and $b variables, which have a special purpose (for sorting).

In general, you should probably try to avoid using the C-style for loop and array subscripts when you can, because it can be made significantly simpler and easier by iterating directly over the values (no off-by-one errors, no out-of-range errors).

my @AoA = ([1, 2, 3], [4, 5, 6], [7, 8, 9]); # an array of arrays for 
+testing purpose
for my $row (@AoA) {
    for my $col (@$row) {
        print "$col ";
    }
    print "\n";
}
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which prints:

1 2 3
4 5 6
7 8 9
[download]

And if you need to make some calculations:

my @AoA = ([1, 2, 3], [4, 5, 6], [7, 8, 9]);
for my $row (@AoA) {
    my ($sum, $count) = (0, 0);
    for my $col (@$row) {
        $sum +=  "$col ";
        $count ++;
    }
    print "Average: ", $sum / $count, "\n" if $count;
}
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which will print the three computed averages:

Average: 2
Average: 5
Average: 8
[download]

Update: The comment about $a and $b was made earlier by zentara, but below in this thread, I had not noticed it when I mentioned that.