What means "Take the tensor product with $\mathbb{Q}$ here?

Question

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I am bit confused, because normally I would have looked at $\mathbb{Z}^k \otimes \mathbb{Q}$, but that does not make sense with the matrices given here. Am I supposed to replace $\mathbb{Z}^2$ by $ \mathbb{Q} \otimes \mathbb{Q}$ here??