Show that g^ij is a contravariant tensor of rank 2.

To show that \( g_{ij} \) is a contravariant tensor of rank 2, we need to demonstrate how it transforms under a coordinate transformation. The metric tensor \( g_{ij} \) is a fundamental object in differential geometry and general relativity, representing the inner product of two vectors in the context of a curved _____ ______ _____ ____ __________ _________ __________ ________ _______ __________ _________.
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