I am trying to calculate the characteristic polynomial of the matrix $n\times n$, $A=\{a_{ij}=1\}$.
When $n=2$, I obtained $p(\lambda)=\lambda^2-2\lambda$ .
In the case $n=3$, $p(\lambda)=-\lambda^3+3\lambda^2$.
For $n=4$, $p(\lambda)=\lambda^4 - 4\lambda^3$.
I guess that for the general case, we have $p(\lambda)=(-1)^n\lambda^{n}+(-1)^{n-1}n\lambda^{n-1}$.
I tried to use induction, but it didn't work, unless I've done wrong
Somebody can help me or give me a hint