Find the multiplicative inverse (reciprocal) of the following rational number:
$$\dfrac{0}{3}$$
Let the reciprocal be $$x$$.
Then, $$\dfrac03\times x=1$$
$$\Rightarrow 0\times x=3$$ [Cross multiplication]
$$\Rightarrow x=\dfrac30$$
But, division by $$0$$ is not defined.
Hence, the reciprocal does not exist.