Final answer:
The multiplicative inverse of 0 does not exist because 0 multiplied by any number is always 0, not 1.
Step-by-step explanation:
The multiplicative inverse of a number x is a number y such that x*y=1.
In order to prove that 0 does not have a multiplicative inverse, we need to show that there is no number y such that 0*y=1.
Let's assume that there exists a multiplicative inverse y for 0. Then, 0*y=1. However, any number multiplied by 0 is always equal to 0, not 1. Therefore, there is no number y that can be the multiplicative inverse of 0.