Group

Given a Binary Operation $\ast$ : $G\times G\to G$ on a set $G$, the pair $(G,\ast )$ is defined as a group if it satisfies the following conditions:

1. $\ast$ is associative.
2. There exists an identity element $e\in G$.
3. For each element $a\in G$, there exists an inverse element $a^{-1}\in G$.

Example

• $G{L}_2(\mathbb{R})$ is the set of all invertible 2×2 matrices, and with matrix multiplication, it forms a group.