If non-zero x is the reciprocal of y, then which of the following may

Sorry for the bad formatting. Let me explain again!
First of all, this is a could be true question:
We are given that \(x = \frac{1}{y}\) or xy = 1
So, let us try to find the value of xy in all the below options:
1)x/(1/y) = x *y = xy = 0.5, which is not 1. So, untrue.
2)(1/x)/y = 1/x * 1/y = 1/xy = 2, xy = 0.5, which is not 1. So, untrue again!
3)(1/y)/x = 1/y * 1/x = 1/xy = 0.5, xy = 1/0.5 = 2, which is not 1. So, untrue again!
4)(1/x)/(1/y) = 1/x * y = y/x = 0.5, this could be true as we are not able to find the value of xy!
5) y/(1/x) = xy = 2, which is not 1. So, untrue!
For the options 1, 2, 3, and 5. We are able to prove that the value of xy is not equals to 1.
However, we are not able to prove or disprove that xy = 1. So, this could be true!

Notice that the question asks which of the following COULD be true, not MUST be true.

x is the reciprocal of y means that x=1/y (y=1/x). Now, replace 1/x by y or 1/y by x in the options:

A. x/(1/y) = 0.5 --> x/x = 0.5 --> 1 = 0.5. WRONG.

B. (1/x)/y = 2 --> y/y = 2 --> 1 = 2. WRONG.

C. (1/y)/x = 0.5 --> x/x = 0.5 --> 1 = 0.5. WRONG.

D. (1/x)/(1/y) = 0.5 --> (1/x)/x = 1/2 --> 1/x^2 = 1/2 --> x^2 = 2. Well, this is possible, if x=2√x=2 or x=−2√x=−2.

E. y/(1/x) = 2 --> y/y = 2 --> 1 = 2. WRONG.

Answer: D.

Hope it's clear.

This is how I solved it:

The two non-zero numbers are: x and y & x = \(\frac{1}{y}\)

A) \(\frac{x}{(\frac{1}{y})}\) = \(xy\) = \({\frac{1}{y}}*y\) = 1 \(\neq{0.5}\)

B) \(\frac{(\frac{1}{x})}{y}\) = \(\frac{y}{y}\) = 1 \(\neq{2}\)

C) \(\frac{(\frac{1}{y})}{x}\) = \(\frac{y}{y}\) = 1 \(\neq{0.5}\)

D) \(\frac{(\frac{1}{x})}{(\frac{1}{y})}\) = \(\frac{1}{x} * \frac{y}{1}\) = \(y^2\)

if y = \(\sqrt{0.5}\) then \(y^2\) = \((\sqrt{0.5})^2\) = \(0.5\) (Possible) (D)

E) \(\frac{y}{(\frac{1}{x})}\) = \(xy\) = \({\frac{1}{y}}*y\) = 1 \(\neq{2}\)