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

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(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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#### Solution Preview

See the attached file.

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

Try n =3 D =2 ...

#### 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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