M_1,M_2\; \in\;M \;, \alpha,\beta \in C \implies A(\alpha M_1\;+\;\beta M_2)=\alpha A M_1 + \beta A M_2= \alpha M_1 A + \beta M_2 A = (\alpha M_1 + \beta M_2) A \implies \alpha M_1 + \beta M_2 \in M