Show that det(A) is a homomorphism from GL(2,R) to R*

[proplaya201]

Homework Statement

let R* be the group of nonzero real numbers under multiplication. then the determinant mapping A-> det(A) is a homomorphism from GL(2,R) to R*. the kernel of the determinant mapping is SL(2,R).
i am suppose to show that this is a homomorphism but i have no idea where to go and what to do

Homework Equations

det(AB) = det(A)det(B)

The Attempt at a Solution

 

[Dick]

If you don't realize that det(AB)=det(A)det(B) basically proves that it is a homomorphism, you might want to look up the definition of homomorphism and think about it.