(There's a slight typo in the question it should say $\Phi : \mathbb{F^n} \rightarrow V$ )
So in this question I can understand the matrix A, which just follows a commutative diagram.
But I don't even know where to start on the actual proof. It appears that $f = \lambda Id_V$ is representative of an eigenvector, but we haven't done eigenvectors yet for this class or up to this point in the textbook, so I don't think eigenvectors and eigenvalues can be used to solve this problem.
It seems to me that the map $f : V \rightarrow V$ is equivalent to $Id_V$
If anyone can give me a hint toward solving this problem that would be great
Thanks