If an operator T on an inner product space, V, has a corresponding unique T as defined in Question 6, then T is said to have an adjoint in V. For two such linear operators, T and R on V, and F, show that (a) (R + T) = R + T , (b) (T) = T , (c) (T R) = RT , (d) (T ) = T (e) for an invertible T, (T )1 = (T 1) (f) im(T )=(ker(T))