If $A$ is singular matrix, then $A\;{\rm{adj}}\;\left( A \right)$

JEE MATHEMATICS MCQ: MATRICES

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A

is singular matrix, then

A\;\mathrm{adj}\;\left( A \right)

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Correct option: B

Is a zero matrix

Option B (Is a zero matrix) is correct because for a singular matrix A, its determinant is 0, and A adj(A) equals |A|I, which results in a zero matrix.

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\left|\begin{array}{ccc}1 & \left(\alpha^{2 x}-\alpha^{-2 x}\right)^2 & \left(\alpha^{2 x}+\alpha^{-2 x}\right)^2 \\ 1 & \left(\beta^{2 x}-\beta^{-2 x}\right)^2 & \left(\beta^{2 x}+\beta^{-2 x}\right)^2 \\ 1 & \left(\gamma^{2 x}-\gamma^{-2 x}\right)^2 & \left(\gamma^{2 x}+\gamma^{-2 x}\right)^2\end{array}\right|

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\omega

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