have at least one correct answer，multiple corrct answers Given an ŉ x n matrix A and a nonsingular nxn matrix P all of whose columns areeigenvectors of A. Which of the following statements are always TRUE? Select all that apply.A is nonsingular.has distinct eigenvalues.AP = PD, for some diagonal matrix D xA is diagonalizable.A has linearly independent eigenvectors. Let A be an n x n matrix that has n distinct eigenvalues A₁, A, with correspondingeigenvectors P₁, P₁. Which of the following statements are always TRUE? Select all thatapply.PLP are mutually orthogonal.A is diagonalizable.A is nonsingular.P₁, P₁ are linearly independent.

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Lis Given an ŉ × ŉ matrix A and a nonsingular nxn matrix P all of whose columns are eigenvectors of A. Which of the following statements are always TRUE? Select all that apply. A is nonsingular. has n distinct eigenvalues. AP= PD, for some diagonal matrix D A is diagonalizable. A has ♬ linearly independent eigenvectors.