3-Dimensional Topological Group

6. Let M = SL(2) be the set of 2 × 2 matrices with unit determinant. Show that,
when regarded as a subset of R4 under
( a b )
( c d ) <-->  (a, b, c, d) Exists R4 and equipped with subspace topology, SL(2) becomes a 3-dimensional topological group. That is, show that (i) SL(2) is a group under matrix multiplication, (ii) SL(2) is a 3-
manifold (find coordinate maps!), and (iii) the multiplication operation (A,B)--> AB−1 is continuous as a mapping from SL(2) × SL(2) ---> SL(2).