show all work and explain it clearly please on paper please its easier to understand

(a) Let A = OT HA OO (i) Find the characteristic polynomial and the eigenvalues of A. State the algebraic multi- plicity of each eigenvalue of A. (Hint: To compute det(A - AI) consider initial steps of applying C1 + C2 and then R2 - R1.) (ii) Find a basis for each eigenspace of A. State the geometric multiplicity of each eigenvalue of A. (iii) The matrix A is diagonalizable. Explain why and then diagonalize A, that is, find an invertible matrix P and a diagonal matrix D such that P-1AP = D. (b) For what values of k E R is the matrix k B = O not diagonalizable? Justify your