Verifying axioms of a group

#group_theory

Let $G$ denote the set of invertible $2 \times 2$ matrices with values in a field. Prove $G$ is a group by defining a group law, identity element, and verifying the axioms. Credit is based on completeness.

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Let $G$ denote the set of invertible $2\times 2$ matrices with values in a field. Prove $G$ is a group by defining a group law, identity element, and verifying the axioms. Credit is based on completeness.