Question

Select all statements below which are true for all invertible n×n matrices A and B

A. AB=BA
B. (A+B)(A−B)=A^2−B^2
C. A+A^−1 is invertible
D. A^3B^8 is invertible
E. (ABA^−1)^4=AB^4A^−1
F. (A+A^−1)^9=A^9+A^−9

Answer 1

The statements that are rue for all invertible n×n matrices A and B are:
(A+B)(A−B)=A^2−B^2
and
(ABA^−1)^4=AB^4A^−1
From the above results we can conclude that the correct options among all the options that are given in the question are option "B" and option "E". I hope the answer helps you.