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JEE MainMathematicsModerateMatrix and determinants

If the adjoint of a 3×3 matrix A is [IMAGE], then
the magnitude of the determinant of matrix A is

Show answer and solution
adj(A)=adj(A) =
∣adj(A)∣=∣A∣3−1=∣A∣2|adj(A)| = |A|^{3 - 1} = |A|^{2}
⇒1(3−7)−4(6−7)+4(2−1)=∣A∣2\Rightarrow 1(3 - 7) - 4(6 - 7) + 4(2 - 1) = |A|^{2}
⇒∣A∣2=−4+4+4=4\Rightarrow |A|^{2} = - 4 + 4 + 4 = 4
∣A∣=±2|A| = \pm 2
Magnitude = 2

Source: Grass-G / M-17 Mathematics Paper 26 Nov Second.docx

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