Hello! I have just one question!

We have the ring $\displaystyle K = M_{2}(\mathbb{Z}_{3}) $, which are all 2x2 matrices over the field $\displaystyle \mathbb{Z}_{3} $. We need to find all the elements of ring $\displaystyle K*$ (the set of multiplicative inverses).

I know that A € K* if the det(A) != 0. But here in Z3 we just have (det(A) == 1) || (det(A) == 2). Just want to know why det(A) == 2 is not the right solution?