Why does the multiplication property of equality not allow us to divide both sides of an equation by zero?

First of all, recall that division by zero is undefined; it's nonsensical; it's just not allowed. So zero certainly needs to be excluded when dividing.

But what about multiplying by zero?

The problem is that multiplying by zero can change the truth of an equation:

It can take a false equation to a true equation.

To see this, consider the false equation '

2 = 3

Multiplying both sides by zero results in the new equation

2 ⋅ 0 = 3 ⋅0 (that is, '0 = 0'), which is true.