Prove that the symmetric matrix is diagonalizable. (Assume that a is real.) 00a --[6] A = 0 a 0 a 00 Find the eigenvalues of A. (Enter your answers as a comma-separated list. Do not list the same eigenvalue multiple times.) λ = Find an invertible matrix P such that P-¹AP is diagonal. P = 11 Which of the following statements is true? (Select all that apply.) OA is diagonalizable because it has 3 distinct eigenvalues. O A is diagonalizable because it has 3 linearly independent eigenvectors. OA is diagonalizable because it is a symmetric matrix. O A is diagonalizable because it has a nonzero determinant. A is diagonalizable because it is an anti-diagonal matrix. A is diagonalizable because it is a square matrix. OA is diagonalizable because it has a determinant of 0.

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