NIMCET 2024 Paper

Section: Mathematics

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Question : 21 of 120

Marks: +1, -0

For an invertible matrix

A

, which of the following is not always true:

${\adj}(A) ≠ 0$
$|A| ≠ 0$
$A A^{-1}=1$
$|A({\adj}(A))| ≠ 1$

Solution:

We know that

|A({\adj}(A))|=|A|^{n-1}

This value should be non-zero, this can be 1 .

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