Actually even I saw $IP^{-1}$ for first time n don't know for sure.. but here by observation..
If you make values as indices and indices as value then you will get $IP^{-1}$
for eg:- in IP at index 0, 5 is present.. then in $IP^{-1}$ at index 5, 0 should be there.
in IP at index 1, 8 is present.. then in $IP^{-1}$ at index 8, 1 should be there... and so on