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Hi,
Let A and B be hermitian operators. Show that C=i[A,B] is hermitian aswell.

Well, I tried just to use the definition but I'm not sure if that's enough (my guess would be no lol).
[tex] C=i[A,B]=iABiBA=iA^\dagger B^\daggeriB^\dagger A^\dagger =i[A^\dagger , B^\dagger ][/tex]
I'm not used to proof stuff as we don't learn it in my degree program.
Is that right, or is that a whole wrong approach?
Thanks for your help
Homework Statement
Let A and B be hermitian operators. Show that C=i[A,B] is hermitian aswell.
Homework Equations

The Attempt at a Solution
Well, I tried just to use the definition but I'm not sure if that's enough (my guess would be no lol).
[tex] C=i[A,B]=iABiBA=iA^\dagger B^\daggeriB^\dagger A^\dagger =i[A^\dagger , B^\dagger ][/tex]
I'm not used to proof stuff as we don't learn it in my degree program.
Is that right, or is that a whole wrong approach?
Thanks for your help