Group/Inverse element/Unique/Fact/Proof
< Group < Inverse element < Unique <
Fact
Proof
Let
x
∘
y
=
y
∘
x
=
e
{\displaystyle {}x\circ y=y\circ x=e\,}
and
x
∘
z
=
z
∘
x
=
e
.
{\displaystyle {}x\circ z=z\circ x=e\,.}
Then we have
y
=
y
∘
e
=
y
∘
(
x
∘
z
)
=
(
y
∘
x
)
∘
z
=
e
∘
z
=
z
.
{\displaystyle {}y=y\circ e=y\circ (x\circ z)=(y\circ x)\circ z=e\circ z=z\,.}
To fact
