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A and B are two square matrices of same ...

A and B are two square matrices of same order. If `AB =B^(-1), " then " A^(-1)` =____.

A

`BA`

B

`A^(2)`

C

`B^(2)`

D

`B`

Text Solution

Verified by Experts

The correct Answer is:
C
`AB = B^(-1)`
`(AB) B = B^(-1) * B`
`AB^(2) =I`
`A^(-1) * A * B^(2) = A^(-1) * I`
`I * B^(2) = A^(-1)`
`therefore A^(-1) = B^(2)`.
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