Given,
$∑$ = { $a, b$}
$L(A)$ = { $x $ $|$ if $x ∊ L(A)$ then $u ∊ L(A)$ for $∃u,v∊∑^{∗}$ where $x = uv $ }
From the given condition, as $v$ contain $\varepsilon$ then $x = u$ and its satisfy all condition ie. if $x ∊ L(A)$ then $u ∊ L(A)$
Therefore,
$L(A)$ $ = (a + b)^{*}$
So, number of final states = $1$