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

If two objects have the same hashcode then they are NOT necessarily equal. Otherwise you will have discovered the perfect hash function.

But the opposite is true: if the objects are equal, then they must have the same hashcode.