6. Indicate whether the following statements are TRUE or FALSE. No partial credit will be given. (a) (5 points) Suppose v is an eigenvector for a 3 x 3 matrix A such that Av = 2v. An eigenvalue for A5 is 32. (b) (5 points) Let A be an (n x n)-matrix. If A is invertible, then the columns of A form an orthonormal basis. (c) (5 points) Let {u1, u2, ..., Un} be an orthonormal basis of R". If v = arul + azu2 + . . . + an Un, then |lu| |2 = a; taz t .. . + an (d) (5 points) Let P be an orthogonal matrix. Then det(P) = 41