A light aircraft instructor reported NMAC with a similar light aircraft that took off behind them and joined up in a formation maneuver without the reporter's knowledge.

Narrative

During climb out of Paeola airport K81; the pilot flying was an instrument student under the hood. Aircraft 1 was climbing to a maneuvering VFR altitude of 5500 MSL. Aircraft 2 departed behind Aircraft 1 from K81. Extreme VFR conditions prevailed and both aircraft departed and remained VFR. After leveling off at 5500 MSL; aircraft 1 received a TA from the on board flight instrument system (FIS) of an aircraft at similar altitude and the same position as aircraft 1 was. After completing a visual scan; the instructor on board aircraft 1 noted aircraft 2 climbing with aircraft 1; matching speed and altitude as to stay at approx. a 4 o'clock position; the aircraft came within 20 feet of aircraft 1's wing tip and matched altitude. After the instructor moved his head; aircraft 2 announced over CTAF 'Made you look' - indicating that aircraft 2 had intentionally flown in formation with aircraft 1 during the climb out and then turned his transponder on; setting off aircraft 1's FIS (Traffic) system. After rocking his wings; aircraft 2 banked 90 degrees to the right and started at 30 degree nose down descent. The TA was then resolved and normal flight continued. To note; no formation flying was discussed prior to the flight or authorized by the PIC/Instructor of aircraft 1.