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1. Show that is A,B are linear operators on a complex vector space V, then their product (or composite) C := AB is also a linear operator on V.

2. Prove the following commutator relationships for Linear Operators A,B,C:

a. [A,B + C] = [A,B] + [A,C]

b. [A,B] = -[B,A]

c. [A,BC] = B[A,C] + [A,B]C

d. [AB,C] = A[B,C] + [A,C]B