Let Vbc an w-dimensional inner product space, and let T and S denote symmetric linear operators on

Question:

Let Vbc an w-dimensional inner product space, and let T and S denote symmetric linear operators on V. Show that:
(a) The identity operator is symmetric.
(b) rT is symmetric for all r in R.
(c) S + T is symmetric.
(d) If T invertible, then T-1 is symmetric.
(e) If ST = TS, then ST is symmetric.