Are two Java objects with same hashcodes not necessarily equal?

Question

I understand why providing same hashcode for two equal (through equals) objects is important. But is the vice versa true as well, if two objects have same hash

Answer 1

To prove , if two objects have the same hashCode does not mean that they are equal

Say you have two user defined classes

    class Object1{
        private final int hashCode = 21;
        public int hashCode(){
            return hashCode;
        }

        public boolean equals(Object obj) {
            return (this == obj);
        }
    }

    class Object2{
        private final int hashCode = 21;
        public int hashCode(){
            return hashCode;
        }

        public boolean equals(Object obj) {
            return (this == obj);
        }
    }

    Object1 object1 = new Object1();
    Object2 object2 = new Object2(); 

    Object1 object3 = new Object1();


    if(object1.hashCode() == object2.hashCode()){
         // return true, because the hashcodes are same
    }

    but 
    if(object1.equals(object3)){
            // will fail, because two different objects   
    }