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## Homework Statement

Find the hermitian conjugates, where A and B are operators.

a.) AB-BA

b.) AB+BA

c.) i(AB+BA)

d.) [itex] A^\dagger A [/itex]

## Homework Equations

[itex] (AB)^\dagger =B^\dagger A^\dagger [/itex]

## The Attempt at a Solution

Are they correct and can I simplify them more?

a.) [itex] (AB-BA)^\dagger = (AB)^\dagger - (BA)^\dagger= B^\dagger A^\dagger - A^\dagger B^\dagger = BA-AB = -(AB-BA) [/itex]

b.) [itex] (AB+BA)^\dagger = (AB)^\dagger + (BA)^\dagger= B^\dagger A^\dagger + A^\dagger B^\dagger = BA+AB [/itex]

c.) [itex] [i(AB+BA)]^\dagger = -i[(AB)^\dagger + (BA)^\dagger]= -i(B^\dagger A^\dagger + A^\dagger B^\dagger) = BA+AB [/itex]

d.) [itex] [A^\dagger A]^\dagger = A^\dagger (A^\dagger)^\dagger=A^\dagger A [/itex]