Find theMöbiustransformation that maps the points $\displaystyle z=1,2,3$ to $\displaystyle w=i,-i,-1. $What are its fixed points?

By a Theorem, I know there's a transformation so that $\displaystyle T(z_j)=w_j$ whenever $\displaystyle z_1,z_2,z_3,w_1,w_2,w_3\in\mathbb C-\{0,1,\infty\},$ so I took a generic transformation given by $\displaystyle w(z)=\frac{az+b}{cz+d},$ so I did $\displaystyle i=\frac{a+b}{c+d},$ $\displaystyle -i=\frac{2a+b}{2c+d}$ and $\displaystyle -1=\frac{3a+b}{3c+d},$ then I think I need to find a relation, or something, how to solve this?