Explicit isomorphism $H_n(\Delta^n, \partial \Delta^n) \cong \mathbb{Z}$

Question

I have read that one can explicitly show that $H_n(\Delta^n, \partial \Delta^n) \cong \mathbb{Z}$ by proving that $$\mathbb{Z} \to H_n(\Delta^n, \partial \Delta^n) \qquad , \qquad n \to [n \cdot \textrm{Id}_{\Delta^n}] $$ is an isomorphism, $n >1$. How should I proceed to show this?