Given a two dimensional Hilbert-space, $\mathcal{H}$, and a vector $\eta \in \mathcal{H}$, of this space,
if $\eta$ transforms in SU(2) like this,
$$\eta \rightarrow e^{(-i\alpha \vec{\sigma}\vec{n}/2)}\cdot \eta$$
$\textbf{Find }$ how does this quantity $${\eta}^{T} i \sigma_{2} \eta$$
$\textbf{transform in SU(2)}.$
(Where $\sigma_{k}$ are Pauli Matrices, $\vec{n}\cdot\vec{n}=1$, $i \in \mathbb{C}$ is the imaginary unit, $\alpha \in \mathbb{R}$ and $\eta^{T}$ is the transpose of the vector $\eta$).
HELP: $i\sigma_{2}\sigma_{i}=-i\sigma^{*}i\sigma_{2}$