Problem 1. 15pts. Determine whether the following statements

Last updated: 7/16/2022

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 F in the box provided under the statement. Do not write "true" or "false". (a) 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) 2 0 must hold. (d) (b) (e) - 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.