AP EAMCET · Maths · Matrices
If \(P\) and \(Q\) are two invertible matrices of the same order, then \(\operatorname{Adj}(Q P)\) is equal to
- A \(|\mathrm{P}||\mathrm{Q}| \mathrm{P}^{-1} \mathrm{Q}^{-1}\)
- B \(|P||Q|(P Q)^{-1}\)
- C \(|P||Q| \operatorname{Adj}(P Q)\)
- D \(|\mathrm{P}||\mathrm{Q}| \operatorname{Adj}(\mathrm{QP})\)
Answer & Solution
Correct Answer
(A) \(|\mathrm{P}||\mathrm{Q}| \mathrm{P}^{-1} \mathrm{Q}^{-1}\)
Step-by-step Solution
Detailed explanation
\(\operatorname{Adj}(QP) = |QP|(QP)^{-1}\) \(\operatorname{Adj}(QP) = |Q||P|P^{-1}Q^{-1}\)
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