We discussed the properties of operators used in quantum mechanics. let us prove some of the identities mentioned there. 1. show that any linear operator î can be represented as l = a + ib. where a and b are hermitian operators (hint: write a and b in terms of l). (2 pt) 2. consider the commutators (a, bc and ab, ĉof any three linear operators a, b, and ĉ. show that they can be expressed via the commutators (a, b], (a, c), and (b, c). (3 pt) 3. consider the following operator, (a-ib)-1. assuming that is small, expand this operator in a power series in 1. hint: write (a - xb)-1 = "în and determine cn. remember that a and b do not necessar- ily commute