Name of this property: if $x * x = y * y \implies x = y$

Question

Algebraically speaking, what's the name of this property?:

$x * x = y * y \implies x = y$

$*$ being a binary operation

Answer 1

Not a full answer...

Define the function $f(x)= x * x$

Then your property is equivalent to $f(x)=f(y) \Rightarrow x=y$

I think that this means that $f(x)$ must be a one-to-one function.

Anyone care to extend / argue?

Answer 2

I would simply say that the operation "$*$" admits uniqueness of square roots.

Just to be clear, following up the comment of Marc van Leeuwen (thanks!), if an element admits a square root, this is unique.

Answer 3

The operation defines an injective squaring operation.