So, hermitian linear operators represent observables in QM. I (a matrix whose elements are all 1) is certainly a hermitian linear operator. Does this mean that I represent a measurable property? If so, what do we call that property? Identity? Moreover, for any state-vector A, A would be an eigenvector of I with the eigenvalue of 1. What does this all mean? What are the physical meaning of I as an observable (if it is) and its eigenvectors and the eigenvalue? How can we 'measure' I to get the value 1?