How to correct a reversed polarity compass:
1 Take a strong magnet, such as a 10x10mm neodymium disc round rare-earth magnet, which work well and are cheap to buy online.
2 Hold the compass flat and horizontal, with the needle floating freely.
3 Take your magnet and, using the south end of the magnet, flick it outwards along the north red needle of your compass.
4 Repeat until your red compass needle points to magnetic north again.
5 Test the accuracy of your compass against another working compass (keeping them 500mm apart).