  Following the work of Gao and Xie in [2], we state some properties of the
inverse Kazhdan-Lusztig polynomial of a matroid. We also give partial answers
to a conjecture that states that regular connected matroids are non-degenerate.
We link the degeneracy of a matroid to the inverse Kazhdan-Lusztig polynomial
and we show that the Conjecture holds for modular matroids, by proving that
degenerate modular matroids are not regular.
