Are you trying to find the eigenvectors? Or are you trying to find the original matrix from its eigenvalues?
In that case, assuming you have three distinct eigenvalues, the best you can do is construct a diagonal matrix similar to A. That is, you can construct a diagonal matrix such that there exists an invertible matrix such that You construct by simply having your 3 eigenvalues on the main diagonal, and zeros everywhere else.
If you have more conditions on A, you might be able to say more than this.