Help me solve this question and please state how you arrived at the answer for learning purposes

Que 1

3 2 2 6 _ _ Let A: and B = . What value(s) of k, if any, Will make -12 -3 k AB=BA? (Z) Select the correct choice below and, if necessary, fill in the answer box within your choice. Q A. k = (Use a comma to separate answers as needed.) Q B. No value of k will make AB = BA 0 1 1 1 Let A: . Construct a 4x2 matrix D, using only 1 and 0 as 1 1 0 1 entries, such that AD =12. Is it possible that CA =14 for some 4 x 2 matrix C? Explain. (:D 1 0 D: 1 1 1 1 Is it possible that CA =14 for some 4 x2 matrix C? Explain. Choose the correct answer below. 0 A- Yes, if C =AT. The product of any m x n matrix and its transpose is I . 111 Q B- No, because if it were true, then CAx would equal x for all x in R4. Since the columns ofA are linearly dependent, Ax = 0 for some nonzero vector x. For such an x, x = Ix = CAx = 0, a contradiction. Hence, CA cannot equal 14. Q C- No, because neither C norA are invertible. When writing 1m as the product of two matrices, since 1m is invertible, those two matrices will also be invertible. C! D- Yes, because C is a 4 x 2 matrix and A is a 2 x4 matrix, making CA a 4 x 4 matrix. For every m x n matrix, there exists an n x m matrix such that the product of the two matrices is Im