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JEE Main 2010 Mathematics question

MathematicsMatricesJEE Main 2010

Let A be a 2 × 2 matrix with non-zero entries and let , where 1 is 2 × 2 identity matrix. Define Tr(A) = sum of diagonal elements of A and |A| = determinant of matrix A. Statement-1: Tr(A) = 0 Statement-2: |A| = 1

Answer: (2)

Solution

With all entries non-zero, , so forces eigenvalues 1 and −1: Tr A = 0 and |A| = −1. (E.g. writing $A =

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Question ID VK-039276