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Q: Let $A$ be an $n\times n$ matrix defined by $A_{ij}=1$ for all $i,j$. Find the characteristic polynomial of $A$.

There is probably a way to calculate the characteristic polynomial $(\det(A-tI))$ directly but I've spent a while not getting anywhere and it seems cumbersome. Something tells me there is a more intelligent and elegant way. The rank of $A$ is only 2. Is there a way to use this?

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    What makes you say the rank is $2$?2012-11-01
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    Related: https://math.stackexchange.com/questions/2853981/find-the-eigenvalues-and-their-multiplicities-of-a-special-matrix?noredirect=1&lq=12018-07-17
  • 0
    Possible duplicate of [Eigenvalues of a matrix of $1$'s](https://math.stackexchange.com/questions/153457/eigenvalues-of-a-matrix-of-1s)2018-07-17

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