I think Text::Table may do what you want. Here is a basic example based on your code.

use strict;
use warnings;
use Data::Dumper;
use Text::Table;

my %data = (
A => { A => 5,  R => -2, N => -1 },
R => { A => -2, R => 7,  N => -1 },
N => { A => -1, R => -1, N => 7 },
);

my @keys = sort keys %data;

my $tb = Text::Table->new( '', @keys );

for my $row (@keys) {
    my @values;
    push @values, $data{$row}{$_} for @keys;
    $tb->load( [$row, @values] );
}

print $tb;


Output 
  A  N  R 
A  5 -1 -2
N -1  7 -1
R -2 -1  7

With A:A changed to 1500
  A    N  R 
A 1500 -1 -2
N   -1  7 -1
R   -2 -1  7
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