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JEE Main 2012 Mathematics question

MathematicsMatricesJEE Main 2012

Let A and B be real matrices of the form and , respectively. Statement 1: AB − BA is always an invertible matrix. Statement 2 : AB − BA is never an identity matrix.

Answer: (2)

Solution

, with determinant . It is singular whenever α = β or γδ = 0, so it is not always

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Question ID VK-103518