only need Q4 solution.. please provide justified solution asap to get a upvote please I need this solution asap in good hand writing and I will give you good feedback thanks

Math 1B03 Assignment 3 Due: October 24, 11:59 PM (EDT) Please submit scans / photographs of your full solutions (if handwritten) or pdfs (if typed) to the Crowchnark dropbox by the above date. You are welcome to discuss these problems with your classmates, but please include an acknowledgement naming any classmate who helped you. 1 4 5 1. Let A = 0 2 6 . Determine for which values of :1: E R the matrix 3:13 A is invertible. 0 3 0 2. An invertible 'n. x 7: matrix A is called orthogonal if AT = Al. (a) If A is orthogonal, what are the only possible values for det A? {b} For each value given in part a, give an example of an orthogonal 2 X 2 matrix with that determinant. Show that your examples are orthogonal. 3. Let A be an n X H singular matrix. Describe one way to construct a non-zero matrix B such that AB = 0n (the n X 1; zero matrix). 4. Let A be an n x n. matrix such that A31 = On. (a) Show that In A is invertible. {b} Let B be an invertible n X a. matrix. Is B A mvertible? Provide a proof if yes, and a counterexample otherwise