$2\times2$ matrix that represents divergence or curl of the space?

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i can't understand the question (d) and (e). for example, curl is a vector but as i know the matrices in the problem is not vectors.

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Is it from Engineering Mathematics 1 course mid-term project?

I don't know how to properly describe d), but for e) I think it means that we just have to choose matrix which rotates vector (i.e acting on vector it rotates it about origin) since curl of a vector is a measure of how much vector wants to be rotated about an axis.