# Thread: Finding the eigenvalues of a matrix

1. ## Finding the eigenvalues of a matrix

Let A be a square matrix of real numbers whose eigenvalues are positive integers.
It is given that |adj(adj(A))| = 81.
What is the characteristic polynomial of the matrix?
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What I did was this:

|adj(adj(A))| = |adj(A)|^(n-1) = |A|^(n-1)^2 = 81

But I don't know how to proceed.
Any suggestions? Or if there's any other possible way...
Thanks!

2. ## Re: Finding the eigenvalues of a matrix

The determinant of A^{n-1} is either -9 or 9.

3. ## Re: Finding the eigenvalues of a matrix

How do I conclude that?

4. ## Re: Finding the eigenvalues of a matrix

Its square is 81.