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Elementary Transformations

If P is a n...

Question

If $P$ is a non singular matrix, then value of $a d j (P^{- 1})$ in terms of $P$ is

A

P / | P |

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B

P | P |

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C

P

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D

none of these

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Solution

The correct option is A $P / | P |$
Given P is non-singular
$| P | \neq 0$
Now, $a d j (P^{- 1}) = (a d j P)^{- 1}$
$= (| P | P^{- 1})^{- 1}$
$= (P^{- 1})^{- 1} | P |^{- 1}$
$= P / | P |$

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