Multiplication and division of each term of a ratio by the same non-zero number

Consider the following statements : 1. If each term of a GP is multiplied by same non-zero number, then the resulting sequence is also a GP. 2. If each term of a GP is divided by same non-zero number, then the resulting sequence is also a GP. Which of the above statements is/are correct?

Show that addition, subtraction and multiplication are binary operations on R but division is not a binary operation on R. Further, show that division is a binary operation on the set R*, of non-zero real numbers.

Multiplication of a non-zero rational number with an irrational number is an irrational number.

Division of fractions the division of a fraction (a)/(b) by a non - zero fraction (c)/(d) is defined as the product of (a)/(b) with the multiplicative inverse or reciprocal of (c)/(d)