Unravel the meaning of the variables to find numerical answers

[AtaraxiaAle]

This is a riddle that has proven to be a stumper.
At least, the people I have asked...

The task is to unravel the meaning of the variables to find numerical answers.
Can you do it?

Solve for "s", "t", "r", and "u:" *Edit* When Zero is not a solution. *Edit*

$$s * s & = & & s \\$$

$$s * t & = & & t \\$$

$$t * r & = & & u \\$$

$$u * u & = & & t \\$$

$$u * r & = & & s \\$$

$$r * r & = & & t \\$$

 

[uman]

s=0
t=0
u=0
r=0

 

[AtaraxiaAle]

Ah, yes, this is true; but not exactly as complicated as it truly is.

I say this, and I should have said this before, because none of these values equal zero.

And! No values "repeat" themselves, exactly.

Try again

 

[DaveC426913]

s=1
t=1
u=1
r=1

Or is that what you mean by "No values repeat themselves, exactly."

 

[Moo Of Doom]

s = 1
t = -1
u = i
r = -i

 

[AtaraxiaAle]

ha-Ha! Yes, that is the correct set of answers "Moo"!

But you can also notice that i and -i can be inter-transposed and still make sense.

Good job.

Yea, if they are all ones then it works as well, but I thought that
was too easy so I said that they shouldn't repeat.