Why HashMap key should be immutable in java

HashMap is used to store the data in key, value pair where key is unique and value can be store or retrieve using the key.
Any class can be a candidate for the map key if it follows below rules.

1. Overrides hashcode() and equals() method.

  Map stores the data using hashcode() and equals() method from key. To store a value against a given key, map first calls key's hashcode() and then uses it to calculate the index position in backed array by applying some hashing function. For each index position it has a bucket which is a LinkedList and changed to Node from java 8. Then it will iterate through all the element and will check the equality with key by calling it's equals() method if a match is found, it will update the value with the new value otherwise it will add the new entry with given key and value.

In the same way it check for the existing key when get() is called. If it finds a match for given key in the bucket with given hashcode(), it will return the value otherwise will return null.
Below picture shows the internal of hashmap.

2. Key class should be immutable.

    If we want to use any class as a key in a hashmap then it should be immutable. If it is not possible then you need to make sure that once the class instance is created it is not modifying those instance properties which participate in the hashcode() calculation and equality check.
Let's understand it by example.
There is an Employee class (mutable) which we want to use as a key in Hashmap.
Employee.java

public class Employee{

    private String name;

    private String id;

    public Employee(String name, String id) {

        super();
        this.name = name;
        this.id = id;
    }

    //public getters
    //public setters
    //hashcode using name & id
    //equals using name & id
}

With this mutable class we create an instance of Employee and put it in a hashmap, for ex:-

Employee key = new Employee("name1", "id1");

hashmap.put(key, "some value");

Let's assume that it has generated some hashcode like 123456 for given name and id, and it has calculated the index as 1 basis on that & then stored the value at related location.

Now we call the setter on name or id on object "key" and it's hashcode is changed, let's assume now it has hashcode as 234567 and index position as 4. for ex:-

key.setName("other name");

If we try to search the map for this key, it may not find a value as it's hashcode is changed and hashmap has calculated different index position for this key.
Now if we call the put() method on map with this key, it will store this object at different position and bucket in the hashmap. It may result in some memory leak as we still have the same employee object (key) as a key in map with the previous hashcode 123456.
Now there are two keys in hash map with the same Employee instance and same name, id but at different positions and bucket. It will make the first key unreachable until we have an instance of Employee with the same name & id as we had during first put which can be used to update or retrieve the value for this key. Below picture describes this scenario step by step which also clarifies why map key should be immutable.