For each pair of rational numbers, given below, verify that the multiplication is commutative:

0 and $\dfrac{-12}{17}$

To prove:

$0 \times \dfrac{-12}{17} = \dfrac{-12}{17} \times 0$

Taking LHS:

$0 \times \dfrac{-12}{17}\\[1em] =\dfrac{0 \times -12}{1 \times 17}\\[1em] =\dfrac{0}{17}\\[1em] =0$

Taking RHS:

$\dfrac{-12}{17} \times 0\\[1em] =\dfrac{-12 \times 0}{17 \times 1}\\[1em] =\dfrac{0}{17}\\[1em] =0$

∴ LHS = RHS

$0 \times \dfrac{-12}{17} = \dfrac{-12}{17} \times 0$