Question

find an interger which when multiplied by -1 and divided by -9 results into reciprocal of that integer​

Answer 1

We can write an equation :

$\frac{-x}{-9} =\frac{1}{x}$

Multiply by 9x :

$x^2=9$

By definition of square root :

$x=3$ or $x=-3$

Two integers are 3 and -3

Verification

$\frac{-3}{-9} =\frac{1}{3}$ verified (The integer 3)

$\frac{3}{-9} =\frac{1}{-3}$ verified (The integer -3)