Irreducible Components of $GL(n,K)$

Question

View $M(n,K)$ as $n^2$-dimensional affine space, and $GL(n,K)$ as the principal open subset defined by the nonvanishing of the polynomial $det$. Then $GL(n,K)$ is an affine variety. What are its irreducible components?

Answer 1

It is irreducible. In fact, any (nonempty) open subset of an irreducible variety is irreducible.