Chapter 3.5, Problem 7E

Find an isomorphism $\varnothing$ from the additive group $\mathbb{Z}$ to the multiplicative group

$H=\left\{\left[\begin{array}{cc}1& n\\ 0& 1\end{array}\right]|n\in \mathbb{Z}\right\}$

and prove that $\varnothing (x+y)=\varnothing (x)\varnothing (y)$.

Sec. $3.4,\#14\gg$

Prove that the set

$H=\left\{\left[\begin{array}{cc}1& n\\ 0& 1\end{array}\right]|n\in \mathbb{Z}\right\}$ is cyclic subgroup of the group $GL(2,ℝ)$.