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If A and B are two square matices such t...

If A and B are two square matices such that AB= A and BA = B, then find `(A^(2006) B^(2006))^(-1)`.

A

`A^(-1) B^(-1)`

B

`B^(-1) A^(-1)`

C

AB

D

Cannot be determined

Text Solution

Verified by Experts

The correct Answer is:
B
(i) If `AB = A, BA = B " then " A^(2) =A, B^(2) = B. `
(ii) `(AB)^(-1) = B^(-1)A^(-1). `
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