Question

{sigma x,sigma y}=0

Answer 1

The Pauli matrices are

$\sigma_x = \begin{pmatrix} 0 & 1\\ 1 & 0 \end{pmatrix}$

$\sigma_y = \begin{pmatrix} 0 & -i \\ i & 0 \end{pmatrix}$

$\sigma_z =\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}$

$\sigma_x \sigma _y = i \sigma_z$

$\sigma_y \sigma_x = - \sigma_x \sigma_y = -i \sigma_z$

The anticommutator of $\sigma_x$ and $\sigma_y$ is

$\{\sigma_x, \sigma_y\} = \sigma_x \sigma_y + \sigma_y \sigma_x = \sigma_x \sigma_y - \sigma_x \sigma_y =0$