A projectivity P (f): RPn→RPn is an involution if P(f) is not the identity and if P(f)◦P(f)=id. Prove that a projectivity P(f):RP1→RP1 is an in volution iff the trace of the matrix off is null. Does...

A projectivity P (f): RPn→RPn is an involution if P(f) is not the identity and if P(f)◦P(f)=id. Prove that a projectivity P(f):RP1→RP1 is an in volution iff the trace of the matrix off is null. Does the above result extend to P1K where K is any field?