you will need two "change of basis" matrices:

P, which changes vectors with coordinates corresponding to the basis {(2,3,0),(1,1,1),(2,3,1)} to vectors with coordinates corresponding to the basis {(1,2,0),(1,1,1),(1,1,0)}.

Q which changes vectors with coordinates corresponding to the basis {(1,1),(1,-1)} to vectors with coordinates corresponding to the basis {(3,-1),(1,-1)}.

if A is your given matrix, then the matrix you want is:

QAP.

what have you done so far?