SQLite: last_insert_rowid() in same INSERT statement

I running this query in PHP/SQLite 3 (PDO)

Scenario: a new driver is inserted into drivers table and an existing car is immediately linked to him:

DRIVERS

• driver_id [PK]


• driver_name

CARS

• car_id [PK]


• 
  

  fk_driver_id [FK]

  
  

  $qr = "INSERT INTO drivers (driver_name) VALUES ('{$_GET['driver_name']}'); COMMIT; UPDATE cars SET fk_driver_id=( SELECT last_insert_rowid() ) WHERE car_id={$_GET['car_id']};"; $stmt = $dbh->prepare($qr); $result = $stmt->execute();

  
  

It inserts the driver but does not UPDATE the cars table and produces no error either.

It works if I use the same query using SQLite Spy.

In PHP it will only if I break it in two parts:

$qr = "INSERT INTO drivers (driver_name) VALUES ('{$_GET['driver_name']}'); COMMIT; ";
$stmt = $dbh->prepare($qr);
$result = $stmt->execute();

$qr = "UPDATE cars SET fk_driver_id=( SELECT last_insert_rowid() ) WHERE car_id={$_GET['car_id']};";
$stmt = $dbh->prepare($qr);
$result = $stmt->execute();

What is wrong in the PHP code if it won't work in one single statement?