Vector Spaces & Bases · Challenge problem

In $P_2$, let $B = \{1,\ x,\ x^2\}$ and $C = \{1,\ x-1,\ (x-1)^2\}$. The change-of-basis matrix $P_{C\leftarrow B}$ has as its columns the $C$-coordinate vectors of $1$, $x$ and $x^2$. Find the sum of all nine entries of $P_{C\leftarrow B}$.