The multiplication map $\mathrm{GL}(n,k)\times\mathrm{GL}(n,k)\to\mathrm{GL}(n,k)$ such that $A\times B\mapsto AB$ is a morphism.

Question

I have to show that the multiplication map $\mathrm{GL}(n,k)\times\mathrm{GL}(n,k)\to\mathrm{GL}(n,k)$ such that $A\times B\mapsto AB$ is a morphism of affine algebraic sets.

I know that given affine algebraic sets $V\subset\mathbb{A}^n$, $W\subset\mathbb{A}^m$ over an algebraically closed field $K$, a map $f:V\to W$ is a morphism if for every $v\in V$, we will get polyomials $p_i\in K[X_1,X_2,\cdots,X_n]$, $i\in\{1,2,\cdots,m\}$ such that $f(v)=(p_1(v),p_2(v),\cdots,p_m(v))$.

So, what are the required polynomials for the multiplication map?

P.S. A hint would be enough.