Tropical algebra is the study of algebraic structures (tropical maps, idempotent semimodules, etc), constructed over the semifield $\underline{\mathbb{R}} = {\mathbb{R}} \cup \{-\infty\}$ with the max operator (resp. usual addition) as 1st (resp.2nd) composition law. After showing first that the concept of injectivity module of a tropical map $A : \underline{\mathbb{R}}^m \rightarrow \underline{\mathbb{R}}^n$ introduced in [Wagneur, E., The Whitney embedding theorem for tropical torsion modules. Classification of tropical modules, Linear Algebra and its Applications, 435, 2011, 1786-1795] fails to be sufficient for the characterisation of Im$A$, we introduce the concept of injectivity domain, and study some of the properties of a matrix $\Gamma^A$ whose columns are given by the saturation of the equivalence class (modulo $A$) of the canonical basis of $\underline{\mathbb{R}}^m$. Numerous examples are provided.