Hey dipsy34.

I'll start you off with a hint: If x is the vector in the standard basis (identity matrix) then we have c = Cx b = Bx where C and B are the change of basis matrix to go from I (identity) to C or B.

Hint: Given the hint try getting c in terms of B,C,b and you will have your answer (remember that you can remove a matrix by pre-multiplying it by its inverse matrix).