Is A a Linear Operator and Hermitian in Quantum Mechanics Postulate 2?

[PAPquestions]

Hi I am new here and also new to QM.

I have encountered a problem about postulate 2 which is the superposition principle. Basically I understand the concept. However, when it comes to real question, I get stuck and can't proceed. Could anyone enlightens me how to get started with the problem below?

Question:
A psi(x) = [psi(x)]^2

Is A a linear operator? Is A a Hermitian?

 

[PAPquestions]

Heh, I found the way to solve it already!

 

[arkajad]

BTW: You should start using the notation $$(A\psi )(x)$$ instead of $$A\,\psi(x)$$. It will help you to understand better the mathematical operations involved.

$$(A\psi )(x)$$ reads: the value of the function $$A\psi$$ at the point x.

Operators act on functions (as objects) and not on values of these functions (numbers).