If you think about it, multiplying two fractions would produce another fraction. An irrational number can't be expressed as a fraction. Thus, multiplying two nationals would produce a rational number.
2) A positive rational number
Let's look at an example
3/4
The reciprocal would be 4/3.
If it is already a positive rational number, turning it upside down wouldn't affect the status of it.
A rational number is a number that can be expressed as a simple fraction. When two rational numbers are multiplied together, the only logical answer would be for the outcome/product to also be rational.
The reciprocal of a positive rational number is also a positive rational number because if the original number was negative, the reciprocal would also be negative since the signs wouldn't change (in this case, the original number is positive). Since the original number is already a rational number, just by flipping it (the reciprocal), it would not change to an irrational, but instead stay the same.
