# I For groups, showing that a subset is closed under operation

1. Feb 20, 2017

### Mr Davis 97

To show that a subset of a group is a subgroup, we show that there is the identity element, that the subset is closed under the induced binary operation, and that each element of the subset has an inverse in the subset.

My question is regarding showing closure. To show that the subset is closed under the operation, if we assume that $a$ and $b$ are elements of the subset , do we have to show that $ab$ is still in he subset or that $ba$ is also in the subset?

2. Feb 20, 2017

### Staff: Mentor

If you show that $ab$ is in the subset for all possible combinations $(a,b)$, does this include $(b,a)\,$?