Similar_Matrices_are_Equivalent

If two square matrices over a ring with unity $R$ are similar, then they are equivalent. It follows directly that every equivalence class for the relation of similarity on $\mathcal M_R \left({n}\right)$ is contained in an equivalence class for the relation of matrix equivalence. Here, $\mathcal M_R \left({n}\right)$ denotes the $n \times n$ matrix space over $R$.