Concatenate any string in $Σ^∗$ with a string $Σ^∗$, you get a string in $Σ^∗$.
No counter example can be found.
Identity? Yes. The null string $\epsilon$
10110 concatenated with what gives null string? There can't be an inverse here.
If you think 10110.$\phi$ would work, then no.
- $\epsilon$ = null string.
- $\phi$ = null set.
Here, inverse doesn't exist for any element except identity element.
So, this is a monoid.