#!/user/bin/perl
use strict;
use warnings;
use Data::Dumper;
use feature 'say';

sub matrix_write_file {
    my ($filename, $matrix) = @_;

    open(my $wfh, '>', $filename)
	or die "Could not open file '$filename' $!";

    # print the whole thing with refs
    for my $aref ( @$matrix ) {
	say $wfh "@$aref";
    }

    close $wfh
	or die "Could not close file '$filename' $!";

    return;
}

sub matrix_read_file {
    my $matrix_name;
    my ($filename) = @_;

    open (my $rfh, $filename)
	or die "Could not open $filename: $!";

    while (my $line = <$rfh>) {
        chomp($line);
        next if $line =~ /^\s*$/; # skip blank lines
        if ($line =~ /^([A-Za-z]\w*)/) {
            $matrix_name = $1;
        } else {
	    my (@row)
		= split (/\s+/, $line);

	    push (@{$matrix_name}, \@row);
		# insert the row-array into
		# the outer matrix array
        }
    }
    close $rfh
	or die "Could not close file '$filename' $!";

    return $matrix_name;
}

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

my $filename = 'matrix.txt';

matrix_write_file($filename, \@matrix);

print Dumper matrix_read_file($filename);

__END__

$ perl test.pl
$VAR1 = [
          [
            '1',
            '2',
            '3'
          ],
          [
            '4',
            '5',
            '6'
          ],
          [
            '7',
            '8',
            '9'
          ]
        ];

$ cat matrix.txt
1 2 3
4 5 6
7 8 9