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If the adjugate of B is A and |P| = |Q| = 1, then the adjugate of Q⁻¹BP⁻¹ equals
- PQ
- QAP
- PAQ
- PA⁻¹Q
Correct answer: PAQ
Solution
adj(Q^-1 B P^-1) = adj(P^-1) adj(B) adj(Q^-1). Since |P|=|Q|=1, adj(P^-1)=det(P^-1)(P^-1)^-1=P and adj(Q^-1)=Q, and adj(B)=A, giving P A Q.
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