Which of the following statements is true about the product of a non-zero rational number and an irrational number?
A.
The product of a non-zero rational number and an irrational number is always an irrational number.

B.
The product of a non-zero rational number and an irrational number is sometimes a rational number.

C.
The product of a non-zero rational number and an irrational number is never an irrational number.

D.
The product of a non-zero rational number and an irrational number is always a rational number.