JEE MainMathematicsModerateMatrix and determinants

Let A is a non - zero matrix of order such that A + adj A =
A^-1 then determinant of (2A^-1) is equal to

Show answer and solution

Pre multiply by A
A^2 + A.adj A = I_2 A^2 +

|A|

.I_2 = I_2

A^{2} = \left( 1 - |A| \right)I_{2}

|A|^{2} = (|A| - 1)^{2}

|A| = \pm (|A| - 1)

\Rightarrow |A| = \frac{1}{2}

Determinant (2A^-1) = 8

Source: Grass-G / M-23 Mathematics Paper 31 Dec FST.docx

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