Question
Question: If A and B are square matrices of same order and A is non-singular, then for a positive integer n(A<...
If A and B are square matrices of same order and A is non-singular, then for a positive integer n(A–1BA)n is equal to-
A
A–n BnAn
B
AnBnA–n
C
A–1BnA
D
n (A–1BA)
Answer
A–1BnA
Explanation
Solution
(A–1BA)2 = (A–1BA) (A–1BA)= A–1B2A
Similarly (A–1BA)n = A–1BnA