JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A\) be any \(3 \times 3\) invertible matrix. Then which one of the following is not always true ?
- A \(adj\, (A)= \left| A \right| . (adj\,(A))^{-1}\)
- B \(adj\, (adj\,(A)) =\left| A \right|.A\)
- C \(adj\, (adj\,(A)) = {\left| A \right|^2} .(adj\,(A))^{-1}\)
- D \(adj\, (adj\,(A)) = \left| A \right|.(adj(A))^{-1}\)
Answer & Solution
Correct Answer
(B) \(adj\, (adj\,(A)) =\left| A \right|.A\)
Step-by-step Solution
Detailed explanation
we know that \(A . a d j A=|A| I_{2}\) \(\operatorname{adj}(\operatorname{adj}(A))=|A|^{n-2} A=|A|^{3-2} A=|A| \cdot A\) so \(3 r d\) is correct using \(a d j A=|A| A^{-1}\) muth is true \(a d j(a d j A)=|a d j A|(a d j A)^{-1}\) \(=|A|^{2}(a d j A)^{-1}\) so 2 nd is true we can…
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