Is matrix a reference to an array (@{$matrix}) or an array (@matrix). You've used both. use strict is your friend. It would have caught that error.

Also, you're always pushing a reference to the same variable (@row) over and over again. All rows of your matrix are going to be the same. The following creates multiple row variables (all named @row). The alternative would be to copy @row into a newly create anon aray by replacing \@row with [ @row ].

#! /usr/bin/perl

use strict;
use warnings;

use Data::Dumper;

my $a = 1; my $b = 2; my $c = 3;  # It's bad to use $a and $b
my $d = 4; my $e = 5; my $f = 6;
my $g = 7; my $h = 8; my $i = 9;

my @matrix;

{
   my @row;
   push(@row, $a);
   push(@row, $b);
   push(@row, $c);
   print "@row\n";
   push(@matrix, \@row);
}

{
   my @row;
   push(@row, $d);
   push(@row, $e);
   push(@row, $f);
   print "@row\n";
   push(@matrix, \@row);
}


{
   my @row;
   push(@row, $g);
   push(@row, $h);
   push(@row, $i);
   print "@row\n";
   push(@matrix, \@row);
}

print(Dumper(\@matrix));
[download]

or

my @matrix = (
   [ 1, 2, 3 ],
   [ 4, 5, 6 ],
   [ 7, 8, 9 ],
);
[download]