Will really appreciate your help with the below question.
I fount that if and $\lambda$ eigenvalue of $A$ then $(1-\lambda)$ is eigenvalue of $A^t$ with the same eigenvectors.
Also if $A=A^t$ then $\lambda=1/2$. I don't know how to proceed (I want to solve it without defining the standard inner product over V, as it was solved originally)
I understand the answer using inner product, I was wondering if there is another solution I could think of because inner product it not the first thing that came to my mind.