Spectral decomposition

Let A i) find the spectral decomposition A. if) find the spectral decomposition of A' and show that the diagonal matrix of eigenvalues is equal to the square of the matrix D found in part (i). ill) find the spectral decomposition of A-1 and show the diagonal matrix of eigenvalues is equal to the inverse of the matrix D found in part (1).Question 4 Let A = -1 1 (a) Calculate AA and find its spectral decomposition. (b) Calculate AA and find its spectral decomposition. (c) Compare the nonzero eigenvalues of A A and those of AAT.A = 6 4 4 i) find the spectral decomposition A. I.e. write A as A = CDC, where D is diagonal matrix of eigenvalues. ii) find the spectral decomposition of A and show that the diagonal matrix of eigenvalues is equal to the square of the matrix D found in part (i). ii) find the spectral decomposition of Aand show the diagonal matrix of eigenvalues is equal to the inverse of the matrix D found in part (i)