Let $A$ be a square matrix of order $n$ whose entries are all integers. Show that every integer eigenvalue of $A$ divides the determinant of $A$.
I am not able to understand how to show this. We know that $\det A$ is the product of eigen values and so every eigen value must divide $\det A$.
But if a matrix has eigen values $3$ and $\frac{4}{3}$ then if I do the product then the factor $3$ gets neutralized if I do the product then how does it appear as a factor of $\det A$?
Please help.