#!/usr/bin/perl
use warnings;
use strict;


my @aminos = qw(a b c);
my $matrix;
my $ratesfromfreq = {a => {a =>  2, b =>  1, c =>  3},
                     b => {a =>  3, b =>  2, c =>  4},
                     c => {a => .4, b => .3, c => .1}};
my $factor = .2;

sub Matrix {
    for my $key (@aminos) {
        for my $key2 (@aminos) {
            $matrix->{$key}{$key2} = $ratesfromfreq->{$key}{$key2} * $
+factor;
        }
        $matrix->{$key}{$key} += (1 - $factor);
    }
    return $matrix;
}


sub printMatrix1 {
    my $matrix2;
    ($matrix2) = @_;
    for my $key (sort keys %$matrix2) {
        print $key . "  " x 2;
        for my $key2 (sort keys %{ $matrix2->{$key}} ) {
            printf '%.5f  ', $matrix2->{$key}{$key2};
        }
        print "\n" x 2;
    }
}

my $P= Matrix();
printMatrix1($P);
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Output:

a    1.20000  0.20000  0.60000

b    0.60000  1.20000  0.80000

c    0.08000  0.06000  0.82000
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thankyou!!

You should use strict and warnings, it would have helped you avoid some trouble.

$matrix is not declared, you should have a my $matrix = {}; at the beginning of the function. This function does not return $matrix. But then again, there are three { block opener but only two } block ends, this doesn't even compile.

To see what's inside a nested data structure (like a hash of hashes), you can use Data::Dumper like this :

use Data::Dumper; #At the top of the file
...
print Dumper $P;
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And at last, you probably want to read perldsc