Question

Suppose that vector v=a(1,1)+b(1,-1) and that vector v=c(2,1)+d(1,2). Compute the matrix M so that (c,d)=M(a,b). I believe that M is suppose to be the transition matrix, but I am having difficulty with setting up. I took the inverse of both (1 1, 1 -1) and (2 1, 1 2) but I do not know which one to use and where to go from there. Please help.