Are static methods inherited in Java?

You can experience the difference in following code, which is slightly modification over your code.

class A {
    public static void display() {
        System.out.println("Inside static method of superclass");
    }
}

class B extends A {
    public void show() {
        display();
    }

    public static void display() {
        System.out.println("Inside static method of this class");
    }
}

public class Test {
    public static void main(String[] args) {
        B b = new B();
        // prints: Inside static method of this class
        b.display();

        A a = new B();
        // prints: Inside static method of superclass
        a.display();
    }
}

This is due to static methods are class methods.

A.display() and B.display() will call method of their respective classes.

All methods that are accessible are inherited by subclasses.

From the Sun Java Tutorials:

A subclass inherits all of the public and protected members of its parent, no matter what package the subclass is in. If the subclass is in the same package as its parent, it also inherits the package-private members of the parent. You can use the inherited members as is, replace them, hide them, or supplement them with new members

The only difference with inherited static (class) methods and inherited non-static (instance) methods is that when you write a new static method with the same signature, the old static method is just hidden, not overridden.

From the page on the difference between overriding and hiding.

The distinction between hiding and overriding has important implications. The version of the overridden method that gets invoked is the one in the subclass. The version of the hidden method that gets invoked depends on whether it is invoked from the superclass or the subclass

Static methods in Java are inherited, but can not be overridden. If you declare the same method in a subclass, you hide the superclass method instead of overriding it. Static methods are not polymorphic. At the compile time, the static method will be statically linked.

Example:

public class Writer {
    public static void write() {
        System.out.println("Writing");
    }
}

public class Author extends Writer {
    public static void write() {
        System.out.println("Writing book");
    }
}

public class Programmer extends Writer {

    public static void write() {
        System.out.println("Writing code");
    }

    public static void main(String[] args) {
        Writer w = new Programmer();
        w.write();

        Writer secondWriter = new Author();
        secondWriter.write();

        Writer thirdWriter = null;
        thirdWriter.write();

        Author firstAuthor = new Author();
        firstAuthor.write();
    }
}

You'll get the following:

Writing
Writing
Writing
Writing book