What does the multiplication axiom of algebra state?

The multiplication axiom of algebra states that if you multiply both sides of an equation by the same non-zero number, the equality of the equation is maintained. This principle is foundational in algebra, allowing for the manipulation of equations in a way that preserves their truth.

When applying this axiom, it is essential that the number used for multiplication is non-zero because multiplying by zero would invalidate the comparison, potentially leading to division by zero in subsequent steps. This axiom enables you to isolate variables and solve equations more effectively, making it an important tool in algebra.

The other options refer to different axioms related to addition and subtraction, or division, which while also valid principles in algebra, do not pertain specifically to the multiplication axiom. Each of these operations has its own axiom that governs the equality of equations when performed on both sides, but in this case, the correct answer specifically addresses multiplication.