R^2/Minkowski form/Orthonormal basis and orthogonal/Determine/Exercise

Suppose that ${}\mathbb {R} ^{2}$ is endowed (beside the standard inner product) with the standard Minkowski form. Determine all bases of ${}\mathbb {R} ^{2}$ that are an orthonormal basis with respect to the inner product and an orthogonal basis with respect to the Minkowski form.

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