Let $V = \mathbb{C}^n$, $A = \Lambda^{\bullet}(\mathbb{C}^n)$ is a graded algebra (with $A_0 = \mathbb{C}, A_1 = V$, etc).

Consider $A_0$ as a left $A$-module, how do we compute the graded ring $\text{Ext}^{\bullet}_A(A_0, A_0)$? (Doing the $n=3$ example should be enough; then it would be easy to generalize.)

(I was trying to understand Koszul duality for symmetric/exterior algebras from [BGS]; and this is the first step.)