Originally Posted byTexasGirlBinary Operation is Closed: The only case where it would not be closed is when,

Thus,

Thus,

Thus,

Impossible, thus the binary operation is closed.

Associative:We have,

And,

Thus,

Identity: We have, that,

and,

.

Inverse: Notice that,

Finally, we need to show if, then, the element

Assume, it were then,

Thus,

Thus,

Thus,

Impossible, thus,