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Define T : P2 → R3 via T(a+bx+cx2) = (a+c,c,b−c), and let B = {1,x,x2} and...

Define T : P2 → R3 via T(a+bx+cx2) = (a+c,c,b−c), and let B = {1,x,x2} and D ={(1, 0, 0), (0, 1, 0), (0, 0, 1)}.
(a) Find MDB(T) and show that it is invertible.
(b) Use the fact that MBD(T−1) = (MDB(T))−1 to find T−1. Hint: A linear transformation is completely determined by its action on any spanning set and hence on any basis.

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