Give an example each, of two irrational numbers, whose product is a rational number

Give an example of each of two irrational numbers, whose quotient is an irrational number.

Prove the following statements stating the field axioms used at each step.

$-(-a)=a$

Prove the following statements stating the field axioms used at each step.

$ab=1\Rightarrow b={\mathrm{a}}^{-1}, \mathrm{a}\ne 0$

Prove the following statements stating the field axioms used at each step.

${\left(a^{-1}\right)}^{-1}=a, a\ne 0$

Prove the following statements stating the field axioms used at each step.

${\left(ab\right)}^{-1}=b^{-1}{a}^{-1}, a\ne 0, b\ne 0$

Prove the following statements stating the field axioms used at each step.

$-(a+b)=-a-b$.