. $I f$ $A$ is non-singular matrix such that $A^{2} = A^{- 1}$ then $a d j A =$

A

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A^{- 1}

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A^{3}

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(A^{- 1})^{2}

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Solution

The correct option is B $A^{- 1}$
$A^{2} = A^{- 1}$
$A . A^{2} = A . A^{- 1}$
$A^{3} = I$
$d e t A . A^{3} = d e t A . I$
$d e t A . A^{3} = A . a d j A$
$d e t A . A^{2} = a d j A$
Therefore
$a d j A = A^{- 1}$ .

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