matrix A for T with respect to the basis B.

B is the basis {v1, v2, v3} of R3 where v1=[1, 1, 1], v2= [2, 3, 0], and v3= [-1, 2, -6] I need to find the matrix A for T with respect to the basis B. But somehow, I can't figure it out. It's given that T: R3--->R3 is a linear transformation and that T(v1)=v2, T(v2)=v3, and T(v3)=v1.

Is T(v1)= [1, 0, 1]? I mean, how do you figure out what T(v) is given the values of v1, v2, and v3? It won't be [(2, 3, 0), (-1, 2, -6), (1, 1, 1)] because that would just be the change of basis right?