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JEE Advanced2014MathematicsMatricesActual

Let M be a 2 × 2 symmetric matrix with integer entries. Then M is invertible if

Options

  1. AThe first column of M is the transpose of the second row of M
  2. BThe second row of M is the transpose of the first column of M
  3. CM is a diagonal matrix with non - zero entries in the main diagonal
  4. DThe product of entries in the main diagonal of M is not the square of an integer

Correct answer

C. M is a diagonal matrix with non - zero entries in the main diagonal

Step-by-step solution

Let M = a c c b (where a, b, c ∈ I ) Then Det M = a b - c 2 If a = b = c , D e t M = 0 If c = 0 , a , b ≠ 0 , D e t M ≠ 0 If a b ≠ square of integer, D e t M ≠ 0

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