session - PHP: Create a simple log in form without MySQL

I'm trying to mess around with a simple log in form, that is just for fun. The content is nothing sensitive, but I'm trying to learnSESSION and such. I've created this simple login form, that works fine, but if a user clicks the"home" button which ishref'd toprocess_login.php, they are asked to login again. I'm trying to save theusername andpassword it in aSESSION so if they login, and hithome from any page, it will remember their log in information and not ask them to continuously log in.

I have aform.php script, that uses thePOST method, with twotextfields, the username and password are saved as "admin" in theprocess_login.php, and if they match thePOSTindices from the form, then i'll includecontent.php. Inprocess_login.php I take thePOST data and run it like so :

SESSION_start();
//var_dump($_POST);
$match_username = 'admin' ;
$match_password = 'admin';

if(isset($_POST['submit'])){
    $username = $_POST['username'];
    $password = $_POST['password'];
    if($username == $match_username && $password == $match_password ){
        include 'content.php';
    }elseif($username == "" || $password != $match_password){
        echo "Please try again.";
    }
    if(!isset($_SESSION["logged_in"])){
        //Run if not set
        $_SESSION["logged_in"] = array(1 => array($username => $_POST['username'], $password => $_POST['password']));
    };
};
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You'll see above that I'm trying to set the SESSION information, but I know i'm not doing it correctly. Once a user logs in, everything works. But if that same user clicks on "home," from another page, it will tell them to "Please try again." I'd like to let the user stay logged in once they are logged in.

All advice is appreciated. Thank you!