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