Problem 1. 15pts. Determine whether the following statements are true or false. If the statement is true, write T in the box provided under the statement. If the statement is false, write Fin the box provided under the statement. Do not write "true" or "false". (a) (b) (c) (d) (e) If A and B are symmetric n x n matrices, then ABBA must be symmetric as well. - If A is an invertible matrix such that A-1=A, then A must be orthogonal. If V is a subspace of R" and is a vector in R", then the inequality (proj) 0 must hold. If matrix B is obtained by swapping two rows of an n x n matrix A, then the equation det (B) - det (4) must hold. There exist real invertible 3 x 3 matrices A and S such that ST AS=-A.