Or, you could just peek in the source of Math::Matrix, nick the transpose() method, un-OO-ify it, and ... voila!

#!perl -l

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

my $transposed = transpose(\@matrix);
local $" = ",";
print "@$_" for @$transposed;


sub transpose {
    my $matrix = shift;
    my @result;
    my $m;

    for my $col (@{$matrix->[0]}) {
        push @result, [];
    }
    for my $row (@{$matrix}) {
        $m=0;
        for my $col (@{$row}) {
            push(@{$result[$m++]}, $col);
        }
    }

    return \@result;
}
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Disclaimer: not my coding style! I just modified existing code to make a point (Use the Source, Luke)