a
(a) $AB = \left[ {\begin{array}{*{20}{c}}0&1\\1&0\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}0&{ - i}\\i&0\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}i&0\\0&{ - i}\end{array}} \right]$
and $BA = \left[ {\begin{array}{*{20}{c}}0&{ - i}\\i&0\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}0&1\\1&0\end{array}} \right] = \left[ {\begin{array}{*{20}{c}}{ - i}&0\\0&i\end{array}} \right] = - AB$
$\therefore AB + BA = O$
Hence, ${(A + B)^2} = {A^2} + {B^2}$.