The court says Kavanaugh took the oath required by the Constitution and another for judges that is part of federal law in the same room where the justices meet for their private conferences.

The 53-year-old justice’s wife, children and parents were in attendance.

Chief Justice John Roberts administered the constitutional oath and retired Justice Anthony Kennedy administered the judicial oath. Kavanaugh is replacing Kennedy on the bench and once served as his law clerk.
I saw where KAVANAUGH considered William Rehnquist - who signed a valid oath - his "judicial hero." What are the chances he signs a valid oath?