Laravel 5.2 Auth relationship

I'm having a problem with a relationship through the Users model when using the Auth class. The relationship I think is suppose to be $this->hasMany('App\Product') and also will it return the newly saved id back to a variable through this method. When I try to use Auth::user()->products()->save($product) I get the following error. I'm learning Laravel 5.2 and I don't know how this code should work could some give me some help

FatalErrorException in ProductsController.php line 32:
Call to a member function products() on a non-object

UserModel:

<?php namespace App;

use Illuminate\Foundation\Auth\User as Authenticatable;
use Zizaco\Entrust\Traits\EntrustUserTrait;
use App\Product;

class User extends Authenticatable
{
    use EntrustUserTrait;

    protected $fillable = [
    'name', 'email', 'password',
    ];

    protected $hidden = [
        'password', 'remember_token',
    ];


    public function products() {
        return $this->hasMany('App\Product');
    }
}

ProductModel:

<?php

namespace App;

use Illuminate\Database\Eloquent\Model;

class Product extends Model
{
    protected $table = "products";

    protected $fillable = ['category_id', 'user_id', 'supplier_id', 'title', 'price'];

    public function user() {
        return $this->belongsTo('App\User');
    }
}

ProductsController:

class ProductsController extends Controller
{

    public function create() {

        $categories = Category::lists('name', 'id')->toArray(); 
        $suppliers = Supplier::lists('company_name', 'id')->toArray();

        return view('products.create', compact('suppliers', 'categories'));
    }

    public function store() {

        $product = new Product(Request::all());

        $id = Auth::user()->products()->save($product);

        return redirect('admin/products');
    }
}

via Chebli Mohamed