Assume an n x n matrix Ais diagonalizable, so A = PDP-1 for some P, with Da diagonal matrix with A1, A2, ..., An along the diagonal. Assume A is invertible, and let B be the inverse of A. It happens that A and B have the same eigenvectors (in fact, a matrix and its inverse always have the same eigenvectors). Find a formula for the inverse of A, making use of P and D as necessary.

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