Let $J_n$ be the $n \times n$ matrix each of whose entries equals 1. Find the nullity and the characteristic polynomial of $J_n$ Let $J_n$ be the $n \times n$ matrix each of whose entries equals 1. Find the nullity and the characteristic polynomial of $J_n$
I got the nullity as 1 and characteristic polynomial as ($\lambda$ -1)
Can anyone please help me for the answer 

Clearly the nullity is $n-1$ since you only need one column to span the image, so the rank is $1$ (apply the dimension theorem, $\text{rank}+\text{nullity}=n$). It follows that $0$ is an eigenvalue with multiplicity $n-1$. 
It is also easy to see that an eigenvalue is $n$: take the all-ones vector $j=(1,\dots,1)$. This is an eigenvector of $J$, with multiplicity $1$ (since all multiplicities add up to $n$). 
Thus the characteristic polynomial is $\lambda^{n-1}(\lambda-n)$.
