Consider (again) the pf5molecule.
(a) what phosphorous atomic orbitals can enter into bonding with the fluorine atoms and how do they transform?
(b) consider the z-axis for each of the fluorines to be along the p-f bond, that is, the fluorine 2pzorbitals are the ones involved in bonding. what is the total, reducible representation corresponding to these orbitals?

it can be observed without changing the identity of the object.

it depends on what substance you're talking about as well as many other factors. in quantum mechanics, the observation of particles affects the observers ability to measure certain properties. for example: you can know the velocity of a particle, but you can't know it's position; or you can know it's position, but not it's velocity. it's like trying to find out where a grain of sand is by throwing other grains of sand at it. once you find out where it is, it's been moved. it's also like trying to find an answer to the question of whether or not a tree falling in a forest makes a sound if nobody is there to hear it. paradoxically, the only way to find out is to be there and hear it.