Alternative way of proving a language is $NP$
It depends on exactly what kind of reduction you're using.  Assuming that you mean a polynomial-time many-one reduction (also called "mapping reductions") then, yes, if $A$&nbsp;reduces to&nbsp;$B$ and $B\in\mathrm{NP}$, then $A\in\mathrm{NP}$, also.  This was probably proven to you when you started to study reductions between $\mathrm{NP}$ problems.

If you mean polynomial-time Turing reduction, it's an open problem whether $A\in\mathrm{NP}$.  This corresponds to the question of whether $\mathrm{NP} = \mathrm{P^{NP}}$.

If you don't know what kind of reduction you mean, you should check with your teacher, but it's probably many-one reductions.  Those are the ones that are most commonly used with respect to problems in&nbsp;$\mathrm{NP}$.