8. Transition Matrices and Similarity. (a) [5pts.] Let A = CD where C and D are nxn matrices and C is invertible. Prove that the matrix product DC is similar to A. Recall DC is similar to A if there is an invertible n x n matrix P such that DC = P-¹AP. (b) [5pts.] Let E = {(1,0), (0, 1)} be the standard basis for R² and 3 = {(1,2), (0, 1)} be a nonstandard basis for R2. Suppose T : R² → R² is a linear transformation whose standard matrix is A = [T] = [T] [J Find [T], which is the matrix of T relative to 3.