JEE Main 2017 Mathematics question

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

Answer: (2)

Solution

Two standard identities for an invertible matrix are

\operatorname{adj}(A) = |A|, \operatorname{adj}(\operatorname{adj}(A)) = |A|^{n-2}A.

For the second becomes , so **option (3) is always true** and **option (4) is the first identity**,

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Question ID VK-115838