Prove that Hermitian/Skew Herm/Unitary Matrix is a Normal Matrix

[Wildcat04]

Homework Statement

Show the proof that the following are all Normal Matrices
a. Hermitian
b. Skew Hermitian
c. Unitary

Homework Equations

Normal Matrices: A*A=AA*
Hermitian Matrices: A=A* or aij=a*ji
Skew Hermitian Matrices A=-A* or aij=-a*ji

The Attempt at a Solution

So far I have tried using the above information for Hermitian Matrices to try and prove that A*A=AA* but I keep getting answers I know not to be correct. I would appreciate a nudge in the correct direction so I can quit pulling my hair out. I have a feeling when I find the correct proof it will be quite obvious, but right now I am just missing something.

 

[Dick]

If A is hermitian then A*=A. A*A=AA=AA*. How are you trying to do it?

 

[Wildcat04]

I was trying to do it much more in depth using a_mn. It never occurred to me to use the basic matrix itself. Like I said, it was right in front of me. Thank you for the help!