suppose $F$ is a forest,prove that the determinant of adjacency matrix of this forest is $-1$ or $0$ or $1$ .
I focused on trees of this forest, say that if I know eigenvalues of trees,I will multiply all together hoping they will be 1 ,-1 or 0.but I don't know anything about them.
in my searching I found useful theorem that say : $T$ is a tree with $n$ vertex,if we have complete matching $det(A)=(-1)^{\frac{n}{2}}$ otherwise it is 0.
1.can you give me some result about eigenvalues of trees.
2.I don't have the proof of theorem I mentioned,can you give me reference to provide it.
3.if I have determinant of trees,if I multiply them, do I have the determinant of forest?
thank you very much.