I have a small script to multiply two matrices together (and no this is not homework, I'm just puttering around with Perl). I have a problem with it that I have been unable to resolve.
matrix_count_rows_cols($r_mat1) is consistently returning 0 rows and 0 columns. Not sure why. Any ideas? (Please keep in mind I'm still pretty green when it comes to Perl). Thanks in advance

use strict 'vars';
use strict 'subs';
use warnings;

my @matrix1=(
    [1, 2, 3], 
    [4, 5, 6],
    [7, 8, 9]
);
my @matrix2=(
    [2, 4, 6],
    [1, 3, 5], 
    [7, 8, 9]
);
print "matrix1=\n";
for (my $i=0;$i le 2;$i++) {
        for (my $j=0;$j le 2;$j++) {
            print $matrix1[$i][$j]," ";
        }
    print "\n";
}
print "matrix2=\n";
for (my $i=0;$i le 2;$i++) {
        for (my $j=0;$j le 2;$j++) {
            print $matrix2[$i][$j]," ";
        }
    print "\n";
}
my @product=matrix_multiply(@matrix1,@matrix2);
print "product=\n";
for (my $i=0;$i le 2;$i++) {
        for (my $j=0;$j le 2;$j++) {
            print $product[$i][$j]," ";
        }
    print "\n";
}
sub matrix_multiply {
    my ($r_mat1,$r_mat2)=@_;
    my ($r_product);
    my ($r1,$c1)=matrix_count_rows_cols($r_mat1);
    my ($r2,$c2)=matrix_count_rows_cols($r_mat2);

    print $c1,$c2,"\n";
    print $r1,$r2,"\n";
    
    die "matrix 1 has $c1 columns and matrix 2 has $r2 rows>" 
        . " Cannot multiply\n" unless ($c1==$r2);
    for (my $i=0;$i<$r1;$i++) {
        for (my $j=0;$j<$c2;$j++) {
            my $sum=0;
            for (my $k=0;$k<$c1;$k++) {
                $sum+=$r_mat1->[$i][$k]*$r_mat2->[$k][$j];
            }
            $r_product->[$i][$j]=$sum;
        }
    }
    $r_product;
}

sub matrix_count_rows_cols { 
    my ($r_mat)=@_;
    my $num_rows=@$r_mat;
    my $num_cols=@{$r_mat->[0]};
    ($num_rows,$num_cols);
}
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