for (...) {
   @row = ();
   ...
   push(@maxtrix, \@row);
}

##</code><code>##

for (...) {
   my @row;
   ...
   push(@maxtrix, \@row);
}

##</code><code>##

use Data::Dumper qw( Dumper );

my $pos = tell(DATA);

{
   my @matrix;

   while (<DATA>) {
      chomp;
      @row = split(/:/, $_);
      push(@matrix, \@row);
   }

   print(Dumper(\@matrix));

   # $VAR1 = [
   #           [
   #             'kaijugal',
   #             '789',
   #             'ghi'
   #           ],
   #           $VAR1->[0],
   #           $VAR1->[0]
   #         ];
}

seek(DATA, $pos, 0);

{
   my @matrix;

   while (<DATA>) {
      chomp;
      my @row = split(/:/, $_);
      push(@matrix, \@row);
   }

   print(Dumper(\@matrix));

   # $VAR1 = [
   #           [
   #             'ikegami',
   #             '123',
   #             'abc'
   #           ],
   #           [
   #             'steverippl',
   #             '456',
   #             'def'
   #           ],
   #           [
   #             'kaijugal',
   #             '789',
   #             'ghi'
   #           ]
   #         ];
}

__DATA__
ikegami:123:abc
steverippl:456:def
kaijugal:789:ghi