Solution

Let a non-zero rational number be \( r \) and an irrational number be \( x \).

If their product \( r \times x \) were rational, then:

\[ x = \frac{r \times x}{r} \]

Since \( r \neq 0 \), dividing a rational number by a rational number would give a rational number.

This would imply \( x \) is rational, which is a contradiction.

Therefore, the product of a non-zero rational number and an irrational number is always irrational.

Final Answer

✔ Correct option: (a) irrational number