1. The problem statement, all variables and given/known data Let R* be the group of nonzero real numbersunder multiplications. 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). 2. Relevant equations 3. The attempt at a solution I know det(A)det(B)=det(AB) but other than knowing that property, I don't understand the meaning of the kernel nor SL(2,R) nor do I understand how GL(2,R) is a homomorphism. I know SL(2,R) stands for Special linear group and GL(2,R) General Linear group.