Let A = 9 -6 0 9 -6 0 4 5 3 eigenspace. (a) Compute the characteristic polynomial pë(λ). (b) Use your answer from part (a) to find all the eigenvalues of A. (c) For each eigenvalue from part (b), find a basis of the corresponding eigenspace. (d) Use your answer from part (c) to determine whether A is diagonalizable. If so, produce an invertible matrix P and a diagonal matrix D such that A = PDP ¹. If not, explain why not in a complete sentence.

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