An elementary proof of Grothendieck's Non-vanishing Theorem

We give an elementary proof of Grothendieck’s non-vanishing Theorem: For a finitely generated non-zero module $M$ over a Noetherian local ring $A$ with maximal ideal $\text{m}$, the local cohomology module $H_{\text{m}}^{\dim M}(M)$ is non-zero.