There is an extra closing bracket that should be removed. You are not checking if your query was successful or not.
$carGroups = mysql_query("INSERT INTO car_groups VALUES('$company','$cars[$i]]')");
should be:
$carGroups = mysql_query("INSERT INTO car_groups VALUES('$company','$cars[$i]')") or die(mysql_error());
Since $cars is an array, you can print its content using print_r or var_dump:
print_r($cars);
var_dump($cars);
Useful reading:
How to get useful error messages in PHP?
mysql_* functions are deprecated