Answer Happy

(1) (7 marks) 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−1B2020A. Justification: True False (b) Let A be an n×n matrix. The set of all n×n matrices X that satisfies (A+A2)X=O is not be closed under the matrix multiplication. True False Justification: (c) If A and B are n×n matrices of rank n, then AB also has rank n. Justification: True □ False
(e) Matrix [33​14​] is invertible when considered as a matrix with entries in R but it is not invertible when considered as a matrix with entries in Z11​. True False Justification: (f) Matrix [21​34​] in Z5​ has two distinct eigenvalues. Justification: False (g) Similar matrices have the same eigenspaces for the corresponding eigenvalues. True □ False Justification: