use Data::Dumper;

my @matrix = (
  [ qw(ab cd ef gh)],
  [ qw(ij kl mn op)],
  [ qw(qr st uv wx)]
);

my @transposed = map {
  my $i = $_;
  [ map $matrix[$_]->[$i], 0 .. $#matrix ]
} 0 .. $#{$matrix[0]};

print Dumper(\@transposed);

__output__

$VAR1 = [
          [
            'ab',
            'ij',
            'qr'
          ],
          [
            'cd',
            'kl',
            'st'
          ],
          [
            'ef',
            'mn',
            'uv'
          ],
          [
            'gh',
            'op',
            'wx'
          ]
        ];