Elementary anticommutation relations

Some non-trivial commutators for elementary second-quantization operators are: $$\begin{array}{rl}& [{\hat{a}}_{p\sigma }^{†},{\hat{a}}_{q\tau }^{†}{\hat{a}}_{r\mu }]=-{\delta }_{pr}{\delta }_{\sigma \mu }{\hat{a}}_{q\tau }^{†}\\ & [{\hat{a}}_{p\sigma },{\hat{a}}_{q\tau }^{†}{\hat{a}}_{r\mu }]={\delta }_{pq}{\delta }_{\sigma \tau }{\hat{a}}_{r\mu }^{†}\\ & [{\hat{a}}_{p\sigma }^{†},{\hat{a}}_{q\tau }{\hat{a}}_{r\mu }]={\delta }_{pq}{\delta }_{\sigma \tau }{\hat{a}}_{r\mu }-{\delta }_{pr}{\delta }_{\sigma \mu }{\hat{a}}_{q\tau }\\ & [{\hat{a}}_{p\sigma },{\hat{a}}_{q\tau }^{†}{\hat{a}}_{r\mu }^{†}]={\delta }_{pq}{\delta }_{\sigma \tau }{\hat{a}}_{r\mu }^{†}-{\delta }_{pr}{\delta }_{\sigma \mu }{\hat{a}}_{q\tau }^{†}.\end{array}$$