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Consider the set of matrices

$$G=\left\{\left(\begin{array}{ll}s & b \\ 0 & 1\end{array}\right): b \in \mathbb{Z}, s \in\{-1,+1\}\right\}$$

Then which of the following is true?

1. $G$ forms a group under addition

2. $G$ forms an abelian group under multiplication

3. Every element in $G$ is diagonalisable over $\mathbb{C}$

4. $G$ is a finitely generated group under multiplication
in Abstract Algebra by Expert | 784 views

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