Question about Proof of Real Number..?

Question

Q: Prove that for any Real Numbers a,b ab=0⇒a=0 or b=0

Answer 1

If ab=x, then a=x/b and b=x/a. When x=0, a=0 or b=0, or a=b=0.

When a and b are real their reciprocals 1/a and 1/b are also real. The product of any number and zero is always zero. x/b is the same as x * 1/b and similarly x/a. When x=0 the product of x and any other number must be zero.