Possible Duplicate:
How to show $\det(AB) =\det(A)\det(B)$
Consider the map $q:\operatorname{GL}(n,R)→R^*$ given by $q(A)=\det(A)$. I know that $$q(AB)=q(A)q(B)=\det(A)\det(B)$$ does not hold if determinants of $A$ and $B$ are not unity. I would like to know why the map is homomorphic?