Question

If $P=[a_{ij}{]}_{n\times n}$ be any matrix and it is non singular matrix. If |P| = |Q| = 1 and adj B = A, then $adj\left(Q^{-1}B{P}^{-1}\right)$ is

• A. QAP
• B. PAQ
• C. AQP
• D. PQA

Answer 1

The correct option is B PAQ

|P| = 1 = |Q| and adj B = A
We know that $\left(adj{P}^{-1}\right)=(adjP{)}^{-1}$
$\therefore \left(adj{Q}^{-1}\right)=(adjQ{)}^{-1}\Rightarrow adj(Q^{-1}B{P}^{-1})=(adj{P}^{-1})adjBadj{Q}^{-1}=(adj{P}^{-1}\left)adjB\right(adjQ{)}^{-1}=\left(P^{-1}{)}^{-1}A\right(Q^{-1}{)}^{-1}$
= PAQ