Hi ALL !!!

First, apology my english !!

Look this problem:

A is a self adjoint operator such that tr(A^2) = 0. Proof that A = 0.

I thought use this property:

<A,B> = tr(B*A)

Because A is a self adjoint operator then I'll have that:

<A,A> = tr(A*A) = tr(AA) = tr(A^2) = 0 => <A,A> = 0 => A = 0.

But, I don't know how show that <A,B> = tr(B*A).

Some one have some idea ???

Thanks a lot !!