Suppose $X$ is a finite simplicial complex and that $H_{*}(X)$ is a free abelian group for each value of $*$. Using the Mayer-Vietoris sequence or otherwise, compute $H_{*}\left(S^{1} \times X\right)$ in terms of $H_{*}(X)$. Use your result to compute $H_{*}\left(T^{n}\right)$.

[Note that $T^{n}=S^{1} \times \ldots \times S^{1}$, where there are $n$ factors in the product.]