If $[\hat{\mathrm{A}}, \hat{\mathrm{B}}]=0$ and $[\hat{\mathrm{A}}, \hat{\mathrm{C}}]=0$, then which of the following necessarily holds: $[\hat{\mathrm{A}}, \hat{\mathrm{B}}$ and $\hat{\mathrm{C}}$ are operators $]$
(a)$[\hat{\mathrm{B}}, \hat{\mathrm{C}}]=0$
(b)$[\hat{\mathrm{A}}, \mathrm{BC}]=0$
(c)$[\hat{\mathrm{B}}, \mathrm{AC}]=0$
(d)$[\hat{\mathrm{C}}, \mathrm{AB}]=0$
Answer
Answer: B ✓ checked by 4AB · confidence high
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
[A, BC] = [A, B]C + B[A, C] = 0; B and C need not commute with each other.