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Find the determinant and inverse of a matrix whose entries are all '1s' ( ones ) except for the diagonals which are '0s' ( zeros )

(1) Let A = (see attachment), the nxn matrix with all entries equal to 1 expect diagonal entries, which are equal to 0. Find the determinant .

(2) For the above matrix A, find the inverse.

Please see attachment for complete questions.

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Expanding the matrix determinant by minors , I obtain for the nxn matrix D = (-1)^(n+1) x (n-1).
Try n =3 D =2
Try n=4 D = ...

Solution Summary

The determinant and inverse of a matrix whose entries are all '1s' ( ones ) except for the diagonals which are '0s' ( zeros ) are found. The solution is detailed.

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