a)I was wrong. The order as seen below is 8. I apologise for my mistake. Hey Ryan, how come you accepted my answer when it was not convincing?EDIT:

b)For the multiplicative inverse to exist , the determinant must be non-zero. Now since the determinant for is . And since , either ad = 1 or bc = 1 is the only possible solution.

Thus the only units are:

With ad = 1,

With bc =1,