I do not own that calculator so I checked the manual. In the chapter Manual calculations it explains the use of matrices but not a single reference to eigenvalues or eigenvectors. I looked also in the advanced functions chapter but nothing on eigenvalues. I believe you will have to use the general algebraic methods for calculating eigenvalues: characteristic polynomial and its solutions. Set up the equation det (Mat A -lambda Mat I)=0 where A is your original matrix and I is the Identity matrix with same dimensions as A. The determinant will give you a polynomial equation in the eigenvalue lambda. the degree of the polynomial will be equal to the dimension of the matrix. You might want to feed the equation to the polynomial solver to find some eigenvalues.
SOURCE: how i can find eigenvalue
In answering your other question I did make a mistake: I looked at the wrong version of the manual. The Algebra FX 2 Plus does solve for eigenvalues. Under the CAS. Here is a screen capture to help you.
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