True or False? Justify your answer. Answers without correct

Last updated: 7/16/2022

True or False? Justify your answer. Answers without correct justification will receive no credit.¹ (a) Let A and B be two square matrices of the same dimension and A be an invertible matrix then (A-¹BA) 2020 = A-¹B2020 A. Justification: True False (b) Let A be an nxn matrix. The set of all nxn matrices X that satisfies (A+ A²)X = 0 is not be closed under the matrix multiplication. Justification: True False (c) If A and B are n x n matrices of rank n, then AB also has rank n. Justification: True False