• Problem 3: (1.5 points) Given  and Ể are Hermitian operators. What can you say about 1. AB 2. Âß + 3. [A, B] 4. i [A,

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• Problem 3: (1.5 points) Given  and Ể are Hermitian operators. What can you say about 1. AB 2. Âß + 3. [A, B] 4. i [A, B] ? Are these operators also Hermitian, anti-Hermitian, non of them, ...? • Problem 4: (1.5 points) It is assumed that you know (1) what a determinant is, (2) that det A* = det A (where t denotes the transpose), (3) that the determinant of a product of matrices is the product of the determinants. Proof, that the determinant of a unitary matrix is a complex number of unit modulus. • Problem 5: (2 points) Verify that the following matrices are unitary: (a) (:1) » (1+117) (1) Verify that the determinant is of the form ei in each case. Are any of the above matrices are Hermitian?