A)$L_{1}=\left \{ a^{n}\,|\, n> 0 \right \} L_{2}=\left \{ b^{n}\,|\, n> 0 \right \}$
Regular language are closed under Concatenation.Hence regular
$L_{1}.L_{2}=\left \{ a^{x}b^{y}\,\,|\,\,x,y > 0 \right \}$
Regular expression-:$a^{+}b^{+}$
B)$L_{2}=\left \{ a^{n}b^{m}\,\,|\,\,n,m \geq 0 \right \}$
Regular Expression-:$a^{*}b^{*}$
Hence regular
C) Not regular need a stack to remember $n$,Thus can't be solved by FSM
Hence not regular