If the == operator returns a true will the equals() method return a true, always?

Yes.

Summary

The following table is a summary. Assume that each row is independent of the others.

code section	pointA == pointB	pointA.equals( pointB )
Point pointA = new Point( 21, 17 ); Point pointB = new Point( 21, 17 );	false	true
Point pointA = new Point( 21, 17 ); Point pointB = new Point( -99, 86 );	false	false
Point pointA = new Point( 21, 17 ); Point pointB = pointA;	true	true

code section

pointA == pointB

pointA.equals( pointB )

Point pointA = new Point( 21, 17 );
Point pointB = new Point( 21, 17 );

false

true

Point pointA = new Point( 21, 17 );
Point pointB = new Point( -99, 86 );

false

Point pointA = new Point( 21, 17 );
Point pointB = pointA;

true

Will pointA.equals(pointB) return the same true/false value as pointB.equals(pointA) ?