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If A and B are square matrices of the same order such that `(A+B)(A-B)=A^(2)-B^(2)` then `(ABA^(-1))^(2)` is equal to

A

`B^(2)`

B

`I`

C

`A^(2)B^(2)`

D

`A^(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given `(A+B)(A-B)=A^(2)-B^(2)`
`impliesA^(2)-AB+BA-B^(2)=A^(2)-B^(2)`
`implies AB=BA`
Now `(ABA^(-1))^(2)=(B"AA"^(-1))^(2)=B^(2)`
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