How works UNIQUE in MySql.sql

CREATE TABLE `Student`
(
 `idStudent` int NOT NULL auto_increment,
 `name`    varchar(45) NOT NULL ,

PRIMARY KEY (`idStudent`)
);

CREATE TABLE `Exam`
(
 `idExam` int NOT NULL auto_increment,
 `name`    varchar(45) NOT NULL ,

PRIMARY KEY (`idExam`)
);



/*
TEST 1
Error Code: 1075. Incorrect table definition; 
there can be only one auto column and it must be defined as a key
*/
CREATE TABLE `StudentExams`
(
 `idStudentExams` int NOT NULL auto_increment,
 `idStudent`        int NOT NULL ,
 `idExam`        int NOT NULL ,

FOREIGN KEY (`idStudent`) REFERENCES `Student` (`idStudent`),
FOREIGN KEY (`idExam`) REFERENCES `Exam` (`idExam`),
PRIMARY KEY (`idStudent`,`idExam`)
);



/*
TEST 2
Unique multiple columns
NB. It doesn't work if a column is NULL, so you can insert multiple rows with those values
*/
CREATE TABLE `StudentExams`
(
 `idStudentExams` int NOT NULL auto_increment,
 `idStudent`        int NOT NULL ,
 `idExam`        int NOT NULL ,

PRIMARY KEY (`idStudentExams`),
FOREIGN KEY (`idStudent`) REFERENCES `Student` (`idStudent`),
FOREIGN KEY (`idExam`) REFERENCES `Exam` (`idExam`)
);
ALTER TABLE `StudentExams` ADD UNIQUE `unique_index`(`idStudent`, `idExam`);



INSERT INTO `Student` (`name`) VALUES ('Mario');
INSERT INTO `Exam` (`name`) VALUES ('Biology');
INSERT INTO `StudentExams` (`idStudent`, `idExam`) VALUES ('1', '1');
INSERT INTO `StudentExams` (`idStudent`, `idExam`) VALUES ('1', '1'); /* ERROR 1062: 1062: Duplicate entry '1-1' for key 'unique_index' */