H_2(GL(2,F)) and Matsumoto's Theorem

Matsumoto's theorem states that for every field F the natural map K_2^M(F) --> K_2(F) from Milnor K-theory to Quillen K-theory in degree 2 is an isomorphism. I will explain Hutchinson's proof of this result which is based on studying the group homology of GL(2,F).