The answers is b) ab≠1, but I have no clue how to get to that answer... Can someone help me?

Your coefficient matrix is
[1 b]
[2a 2].

The condition for a unique solution is that your coefficient matrix is invertible, ie (1)(2) - (2a)(b) does not equal 0. Setting 2 - 2ab = 0, we get 2(1 - ab) = 0. So ab cannot equal 1.

Seriously?

Yes Seriously, GeorgeLucas.
Thanks to Imperious for the reply.
I have also asked for the help domyhomeworkfor.me site, and got the solution:
this can easily be done with determinants. If a square matrix's determinant does not equal zero, then that square matrix will have an inverse hence having a unique solution. Since this is a 2x2 matrix, just compute the determinant with the condition that it cannot equal zero:
(1)(2)-(2ab) =/= 0
2 =/= 2ab
1=/= ab