Dense 2-generator subsemigroups of \(2 \times 2\) matrices (Q645372)

The author, using elementary linear algebra, constructs some explicit examples of dense subsemigroups with two generators of \(GL(2,\mathbb{R})\), \(SL(2,\mathbb{R})\) and \(GL(2,\mathbb{C})\). He also shows that the semigroup of all real linear fractional transformations on a proper subinterval of the real line does not admit any dense subsemigroup with two generators and then he constructs a family of examples of dense subsemigroups with three generators.