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Maths-

General

Easy

Question

A and B are square matrices and A is non-singular matrix, (A–1BA)n, n $element of$ I⁺, is equal to

A^–nBⁿAⁿ
AⁿBⁿA^–n
A^–1BⁿA
A^–nBAⁿ

The correct answer is: A^–1BⁿA

For n = 2 $rightwards double arrow$ (A^–1 BA) (A^–1BA) = A^–1B²A
(A^–1 BA)³ = (A^–1BA)² (A^–1BA) = (A^–1B²A) (A^–1BA)
= A^–1B³A and so on thus (A^–1BA)ⁿ = A^–1BⁿA

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