A(1), A(2), A(3), ……, A(n) " and " B(1),...

`A_(1), A_(2), A_(3), ……, A_(n) " and " B_(1), B_(2), B_(3), …., B_(n)` are non-singular square matrices of order n such that `A_(1)B_(1) = I_(n), A_(2)B_(2) = I_(n), A_(3)B_(3) = I_(n),……A_(n)B_(n) = I_(n) " then"(A_(1) A_(2)A_(3)….. A_(n))^(-1)` = ______.

`B_(1)B_(2)B_(3)… B_(n)`

`B_(1)^(-1)B_(2)^(-1)B_(3)^(-1)… B_(n)^(-1)`

`B_(n)B_(n)-_(1)B_(n)-_(2)….B_(1)`

`B_(n-1)B_(n-1^(-1)) B_(n-2^(-1))...B_(1)^(-1)`

Text Solution

Verified by Experts

The correct Answer is:

(i) `AB = I rArr A^(-1) = B`.
(ii) `(AB)^(-1) = B^(-1)A^(-1)`

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