1. The problem statement, all variables and given/known data C= a -b b a and p is the mapping Complex numbers --> C by the rule p(a+ib)= a -b b a Show that p is a bijection 2. Relevant equations 3. The attempt at a solution Well I need to prove it is both injective and surjective. For Injectivity I have tried showing that the determinate=0, but all I got was detA=a^2 + b^2 and for surjectivity. I also know that any non square matrix cannot be bijective, so attempted to involve this in the answer, but I don't think this is the right thing to be doing. I have no idea what to do. I have not tackled questions similar to this before, so don't really have any idea what path I should be following. Any help hugely welcome.