First slide

Applications of determinant

Question

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

Moderate

A

P/|P|
B

P|P|
C

P
D

none of these

Solution

We know that for any non-singular matrix A,
$A^{- 1} = \frac{1}{| A |} a d j (A)$
$Now put A = P^{- 1} . Then we have$
$\begin{aligned} {(P^{- 1})}^{- 1} = \frac{1}{|P^{- 1}|} a d j (P^{- 1}) \\ \Rightarrow P = | P | adj (P^{- 1}) \\ \Rightarrow adj (P^{- 1}) = \frac{P}{| P |} \end{aligned}$

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