Let V = M_n(C) (so V is a n^2 dimensional vector space). Consider the inner product on V given by 〈A, B〉 = tr(B^∗ A). Fix M ∈ V . Define T : V →V as T (A) = M A. (i) Prove that T is self adjoint if and only if M is self adjoint. (ii) Prove that T is normal if and only if M is normal. (iii) Prove that T is unitary if and only if M is unitary.

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