If operatorname{adj} B = A and |P| = |Q| = 1, | vedclass

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(C) We know that for any invertible matrix $M$,$\operatorname{adj}(M) = |M| M^{-1}$.Let $M = Q^{-1} B P^{-1}$.Then $\operatorname{adj}(M) = |Q^{-1} B

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(C) We know that for any invertible matrix $M$,$\operatorname{adj}(M) = |M| M^{-1}$.Let $M = Q^{-1} B P^{-1}$.Then $\operatorname{adj}(M) = |Q^{-1} B P^{-1}| (Q^{-1} B P^{-1})^{-1}$.Using the properties of determinants $|XY| = |X||Y|$ and $|X^{-1}| = \frac{1}{|X|}$,we have $|Q^{-1} B P^{-1}| = |Q^{-1}| |B| |P^{-1}| = \frac{1}{|Q|} |B| \frac{1}{|P|}$.Since $|P| = 1$ and $|Q| = 1$,we get $|Q^{-1} B P^{-1}| = |B|$.Now,calculating the inverse: $(Q^{-1} B P^{-1})^{-1} = (P^{-1})^{-1} B^{-1} (Q^{-1})^{-1} = P B^{-1} Q$.Substituting these into the adjoint formula:$\operatorname{adj}(Q^{-1} B P^{-1}) = |B| P B^{-1} Q$.Since $\operatorname{adj} B = |B| B^{-1} = A$,we substitute $A$ for $|B| B^{-1}$.Therefore,$\operatorname{adj}(Q^{-1} B P^{-1}) = P A Q$.

If $\operatorname{adj} B = A$ and $|P| = |Q| = 1$,then $\operatorname{adj}(Q^{-1} B P^{-1}) = $

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