If adj B = A , |P| = |Q| = 1, then adj (Q-1BP-1) is

Question

If adj B = A , |P| = |Q| = 1, then adj (Q-1BP-1) is (A) PQ (B) QAP (C) PAQ (D) PA-1Q

Tardigrade Admin · Accepted Answer

Given adj B = A , |P| = |Q| = 1 Consider , adj (Q-1 BP-1) = (adj P-1) (adj B) (adj Q-1) = (adj P)-1 A.(adj Q)-1 = (P-1)-1 A(Q-1)-1 (∵ P-1 = (1/|P|) . adj P ) = PAQ .

Q. If $a d j B = A, ∣ P ∣ = ∣ Q ∣ = 1$ , then $a d j (Q^{- 1} B P^{- 1})$ is

$PQ$

$Q A P$

$P A Q$

$P A^{- 1} Q$

Given $a d j B = A, ∣ P ∣ = ∣ Q ∣ = 1$
Consider , $a d j (Q^{- 1} B P^{- 1})$
$= (a d j P^{- 1}) (a d j B) (a d j Q^{- 1})$
$= (a d j P)^{- 1} A . (a d j Q)^{- 1}$
$= (P^{- 1})^{- 1} A (Q^{- 1})^{- 1} (∵ P^{- 1} = \frac{1}{∣ P ∣} . a d j P)$
$= P A Q .$

Q. If adjB=A,∣P∣=∣Q∣=1, then adj(Q−1BP−1) is

PQ

QAP

PAQ

PA−1Q