  This paper is a continuation of [arXiv:1603.02204]. Exploded layered tropical
(ELT) algebra is an extension of tropical algebra with a structure of layers.
These layers allow us to use classical algebraic results in order to easily
prove analogous tropical results. Specifically we prove and use an ELT version
of the transfer principal presented in [2]. In this paper we use the transfer
principle to prove an ELT version of Cayley-Hamilton Theorem, and study the
multiplicity of the ELT determinant, ELT adjoint matrices and quasi-invertible
matrices. We also define a new notion of trace -- the essential trace -- and
study its properties.
