Corollaire

Let $\lambda \in k$. If $\lambda$ annihilates $M$ or $N$, then it annihilates $\operatorname{Ext}_A(M,N)$. Indeed, $\lambda \cdot 1_{\operatorname{Ext}_A(M,N)} = \operatorname{Ext}_A(\lambda 1_M, 1_N) = \operatorname{Ext}_A(1_M, \lambda 1_N)$.