The matrix A is given by A = [[2, 2, -3], [2, 2, 3], [-3, 3, 3]] The matrix A has an eigenvector [[1], [-1], [1]]. Find the corresponding eigenvalue. The matrix A also has eigenvalues 4 and 6. Find corresponding eigenvectors. Hence find a matrix P such that A = PDP⁻¹, where D is a diagonal matrix which is to be determined. The matrix B is such that B = QAQ⁻¹, where Q = [[4, 1, 5], [1, 4, 2], [1, 2, 1]] By using the expression PDP⁻¹ for A, find the set of eigenvalues and a corresponding set of eigenvectors for B.