formula

$T_{1}J_{3}=\left[ \begin{array}{cc} 1 &0\\ 0&-1 \\ \end{array} \right] \left[ \begin{array}{c} 1 \\ j \\ \end{array} \right] = \left[ \begin{array}{c} 1 \\ -j \\ \end{array} \right] = J_{2}$