Find the multiplicative inverse (or reciprocal) of:

$\dfrac{0}{2}$

To find the multiplicative inverse (or reciprocal) of a non-zero rational number, interchange its numerator and denominator.

Here $\dfrac{0}{2} = 0$, and there is no rational number which when multiplied by 0 gives 1.

Hence, the multiplicative inverse of $\mathbf{\dfrac{0}{2}}$ does not exist.