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Properties of Determinants

A and B are t...

Question

A and B are two square matrices of same order. If $A B = B^{- 1}$ , then $A^{- 1}$ =

A

B A

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B

A^{2}

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C

B^{2}

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D

B

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Solution

The correct option is C $B^{2}$
$A B = B^{- 1}$
$(A B) B = B^{- 1} . B$
$A B^{2} = I$
$A^{- 1} . A . B^{2} = A^{- 1} . I$
$I . B^{2} = A^{- 1}$
Therefore, $A^{- 1} = B^{2}$ .

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