Computation of the induced linear map by the exterior product

Question

Given a matrix $$A:V\to V$$ and an integer $k$, is there a way of having the corresponding $$\wedge^k A: \wedge^k V \to \wedge^k V$$ computed by Maple? This question is linked with Calculating the map "induced" by the exterior product? but my problem is that when the dimension of $V$ and $k$ are growing, it becomes rapidly unreasonable to do this computation by hand.