<p>In this manuscript, we explore the characterization of free modules. Initially, we establish that the collection of <i>n</i>-dimensional rhotrices, composed of elements from any module over a commutative ring with unity, constitutes a module through rhotrix addition and heart base multiplication. Moreover, we demonstrate the existence of a basis for <i>n</i>-dimensional rhotrix free modules, corresponding to the basis of any arbitrary free module. Additionally, we prove a one-to-one correspondence between the bases of rhotrix free modules and arbitrary free modules. Furthermore, we define rhotrix module homomorphism and Schur’s lemma for simple rhotrix modules.</p>