Homomorphisms and Isomorphisms · Medium problem

Let $GL(2, \mathbb Z_3)$ denote the group of invertible $2 \times 2$ matrices with entries in $\mathbb Z_3$. The determinant map $\det: GL(2, \mathbb Z_3) \to U(3)$ is a group homomorphism (with $U(3) = \{1, 2\}$ under multiplication). How many matrices are in the kernel of this homomorphism?