? If \hat{A} and \hat{B} are two commuting operator.
proof that
i) [\hat{A}, \hat{B}] + [\hat{B}, \hat{A}] = 0
ii) [\hat{A}, \hat{A}] = 0
iii) [\hat{A}, \hat{B} + \hat{C}] = [\hat{A}, \hat{B}] + [\hat{A}, \hat{C}]
iv) [\hat{A} + \hat{B}, \hat{C}] = [\hat{A}, \hat{B}] + [\hat{B}, \hat{C}]
v) [\hat{A}, \hat{B}\hat{C}] = [\hat{A}, \hat{C}]\hat{B} + \hat{A}[\hat{B}, \hat{C}]