Suppose that operators A^ and B^ are both Hermitian, i.e, A^` = A^ and B^` = B^.
Answer the following and show your work:

(a) Is A^² Hermitian?
(b) Is A^B^ Hermitian?
(c) Is A^B^+ B^A^ Hermitian?
(d) Is it possible for A^ to have complex eigenvalues, or must they be real?

This can be defined as a matrix whose elements are real and symmetrical i.e. it a square matrix that is equal to its own conjugate, or we can simply put that its a matrix in which those pairs of element that are symmetrically placed with respect to the principal diagonal are complex conjugates.i.e the diagonal elements( Hermitian operators) are real numbers while others are complex numbers.

The solution to the question above are on the first and second uploaded image.

Suppose that operators A^ and B^ are both Hermitian, i.e, A^` = A^ and B^` = B^. Answer the following and show your work: (a) Is A^² Hermitian? (b) Is A^B^ Hermitian? (c) Is A^B^+ B^A^ Hermitian? (d) Is it possible for A^ to have complex eigenvalues, or must they be real?

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Suppose that operators A^ and B^ are both Hermitian, i.e, A^` = A^ and B^` = B^.
Answer the following and show your work:

(a) Is A^² Hermitian?
(b) Is A^B^ Hermitian?
(c) Is A^B^+ B^A^ Hermitian?
(d) Is it possible for A^ to have complex eigenvalues, or must they be real?