Closed subgroup of algebraic group inherits algebraic group structure

Statement
Suppose $$G$$ is an algebraic group over a field $$K$$ and $$H$$ is a closed subgroup of $$G$$. Then, $$H$$ inherits the structure of an algebraic group from $$G$$: the group structure is simply as a subgroup, and the variety structure arises on account of being a closed subvariety of the algebraic variety $$G$$.