Thanks a lot. I found my mistake. The updated code for sorting the sum and then printing the ids as well as the column values too is as follows:

sub sort {
    my ($INPUT, $OUT) = @_;
    my %data;
    
    while (<$INPUT>) {
        next if (/^I|A|M/);
        chomp;
        my ($id,@cols) = split ('\t',$_);
        push @{$data{$id}}, \@cols; 
    }
    
     my %hash;
     my $arrrow;
     my @arrcol;
       
    for my $key (keys %data){
        for my $aref(@{$data{$key}}){
            my $sum = sum(@{$aref});
            my @col = @$aref;           
            push @{$hash{$sum}{$key}}, \@col;
        }
    }
    
    for my $sum (sort keys %hash){
        for my $key(sort keys %{$hash{$sum}}){
            for my $val (@{$hash{$sum}{$key}}){
                 print $OUT "$key\t$sum\t@{$val}\n";               
            } 
        }
    }
}
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