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I'm stuck with this excercise that is asking me to proof that the determinant of the nxn matrix with a's on the diagonal and everywhere else 1's equals to:

|A| = (a + n - 1).(a-1)^(n-1)

So the matrix should look something like:

[a 1 1.. 1]

[1 a 1.. 1]

[: ....... :]

[1 ..1 1 a]

I started subtracting row n-1 from row n, row n-2 from row n-1 and so on. But this gives me a matrix with a bidiagonal part (if that's the correct term, probably not!) under the first row. This looks needlessly complicated, and I don't know how to go from there. Maybe I did it the wrong way..

I would appreciate any help.

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# Determinant of this symmetric matrix (proof)

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