Here is one way:

    #!/usr/bin/perl -wl

    use strict;
    use Data::Dumper;

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

    my @transpose;
    for my $aref (@matrix) {
        my $i = 0;
        push @{$transpose[$i++]}, $_ for @$aref;
    }

    print Dumper(@matrix);
    print Dumper(@transpose);

    __END__
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--
John.