2. (10 pts) Consider the following subspace U = {A Man | PAP is diagonal} where P e Man is a fixed, invertible matrix. (a) Let P = 2 3 Find a basis for U. (Hint: you may want to do part (b) first.) (b) For a general invertible Pe Men, find a basis for U using the following process: 1. Let Vc Man be the set of diagonal matrices and show that T' : U - V is an isomorphism where T(A) = P-'AP 2. Find a basis { D1, D2, ..., Dx} for V (you have to figure out what k should be as well). 3. Map the basis for V back to a basis for U by applying T