If $[\widehat{A}, \widehat{B}]=0$ and $[\widehat{A}, \widehat{C}]=0$, then which of the following necessarily holds: $[\widehat{A}, \widehat{B}$ and $\widehat{C}$ are operators]
(a)$[\widehat{B}, \widehat{C}]=0$
(b)$[[\widehat{A}, \widehat{B C}]=0$
(c)$[\widehat{B}, \widehat{A C}]=0$
(d)$[\widehat{C}, \widehat{A B}]=0$
Answer
Answer: B ✓ checked by 4AB · confidence high
Explanation
[A, BC] = [A, B]C + B[A, C] = 0 + 0. Nothing forces B and C to commute with each other, so the other options need not hold.