Does order of columns of Multi-Column Indexes in where clause in MySQL matter?

I have a table below:

CREATE TABLE `student` ( 
     `name` varchar(30) NOT NULL DEFAULT '',
     `city` varchar(30) NOT NULL DEFAULT '', 
     `age`  int(11) NOT NULL DEFAULT '0',
     PRIMARY KEY (`name`,`city`) 
 ) ENGINE=InnoDB DEFAULT CHARSET=utf8;

I want to know, if I execute the following two SQLs, do they have the same performance?

mysql> select * from student where name='John' and city='NewYork';
mysql> select * from student where city='NewYork' and name='John';

Involved question:

1. If there is a multi-column indexes (name, city), do the two SQLs all use it?
2. Does the optimizer change the second sql to the first because of the index?

I execute explain on the two of them, the result is below:

mysql> explain select * from student where name='John' and city='NewYork';
+----+-------------+---------+-------+---------------+---------+---------+-------------+------+-------+

| id | select_type | table   | type  | possible_keys | key     | key_len | ref         | rows | Extra |
+----+-------------+---------+-------+---------------+---------+---------+-------------+------+-------+

|  1 | SIMPLE      | student | const | PRIMARY       | PRIMARY | 184     | const,const |    1 | NULL  |
+----+-------------+---------+-------+---------------+---------+---------+-------------+------+-------+

mysql> explain select * from student where city='NewYork' and name='John';

+----+-------------+---------+-------+---------------+---------+---------+-------------+------+-------+
| id | select_type | table   | type  | possible_keys | key     | key_len | ref         | rows | Extra |
+----+-------------+---------+-------+---------------+---------+---------+-------------+------+-------+

|  1 | SIMPLE      | student | const | PRIMARY       | PRIMARY | 184     | const,const |    1 | NULL  |
+----+-------------+---------+-------+---------------+---------+---------+-------------+------+-------+