Let A be any 3 × 3 invertible matrix. Then which one of the following is not always true?

1. $adj \left(adj\mathrm{ (A)}\right)={\left|A\right|}^2. {\left(adj\mathrm{ (A)}\right)}^{-1}$
2. $adj \left(adj\mathrm{ (A)}\right)=\left|A\right|.{\left(adj\mathrm{ (A)}\right)}^{-1}$
3. $adj \left(ad\mathrm{j\; (A)}\right)=\left|A\right| . A$
4. $adj\mathrm{ (A)}=\left|A\right|.A^{-1}$

Solution

Asked in: JEE Main 2017 (08 Apr Online)

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