Given $r=a^{*}(a+b)$ over $=\{a,b\},$ what is $L(r)?$

Use the following recursive rules and include all steps.

$L()=$

$L()=\{\}$

$L(a)=\{a\},$ where a is a symbol that belongs to the alphabet.

$L(r_1+r_2)=L(r_1)L(r_2)$

$L(r_1{r}_2)=L(r_1)L(r_2)$

$L[(r)]=L(r)$

$L(r^{*})=[L(r){]}^{*}$