Don't know how to do these questions

(b) A E Mm) be normal. Show that if All)\" = Anus! then A is an orthogonal projection matrix. (e) Let V be a nite dimensional inner product space, and let H C V be an invariant subspace of a normal operator L E fz', V). Let P = ProjH be the orthogonal projection. Show that PL = PLP. (:31) Let A E MHXAC) be innertible. Show that A2131 is diagonalizable 1:} A is diagonalizable. (Hint: Use the fact that the polynomial t\" A for A 79 D has n distinct root.)