A Hyperbolic Metric

The Poincare half-plane model for hyperbolic space puts the following metric on the plane:

$ds^2 = \frac{1}{y^2} (dx^2 + dy^2).$

Compute the Ricci scalar $R$ for this metric in matrix form. Is this a vacuum solution to Einstein's equations?

Give your answer as an $(R,$ Yes/No$)$ pair.

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