# eigen values and eigen vector of a matrix [duplicate]

Let $A$ be an n *n matrix all of whose entries are 1. Find all the eigenvalues and eigenvectors of $A$. I have checked for 2*2 ,3*3 matrices and guessing the answer but in general how to show.

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## marked as duplicate by apnorton, Michael Albanese, hardmath, Salech Alhasov, PhiraJan 10 '14 at 17:26

• The dimension of the kernel of $A$ is $n-1$ (why?) so $0$ is an eigenvalue with multiplicity $n-1$;
• For the eigenvectors solve the equation $$Ax=\lambda x$$ for $\lambda$ the two founded eigenvalues.