(i) Consider the group $G=G L_{2}(\mathbb{R})$ of all 2 by 2 matrices with entries in $\mathbb{R}$ and non-zero determinant. Let $T$ be its subgroup consisting of all diagonal matrices, and $N$ be the normaliser of $T$ in $G$. Show that $N$ is generated by $T$ and $\left(\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right)$, and determine the quotient group $N / T$.

(ii) Now let $p$ be a prime number, and $F$ be the field of integers modulo $p$. Consider the group $G=G L_{2}(F)$ as above but with entries in $F$, and define $T$ and $N$ similarly. Find the order of the group $N$.