Remembering that the core stems from an orthogonal model,
we know that the square of the elements is proportional to the variation explained by the corresponding factor combination.
Ergo, the three elements having the values
96.27, -18.34 and 13.08 each represent the three most important factor combinations.
Note that the remaining factor combinations can be regarded as being insignificant in the model of X.
We see that the elements
correspond to indices (1,1,1), (1,2,2) and (1,3,3).
From these combinations we see that there is one very important factor, namely factor one in the first mode (i.e. the first column of component matrix A).
This factor is a part of all the significant factor combinations.