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JEE Main202229 Jul 2022Morning ShiftMathematicsMatricesActual

Let A and B be two 3 × 3 non-zero real matrices such that A B is a zero matrix. Then

Options

  1. AThe system of linear equations A X = 0 has a unique solution
  2. BThe system of linear equations A X = 0 has infinitely many solutions
  3. CB is an invertible matrix
  4. Dadj A is an invertible matrix

Correct answer

B. The system of linear equations A X = 0 has infinitely many solutions

Step-by-step solution

Given, A B = 0 ⇒ A B = 0 If A ≠ 0 ,   B = 0 (not possible) If B ≠ 0 ,   A = 0 (not possible) Hence A = B = 0 So, if A = B = 0 then A   &   B are non-invertible matrix, So, A X = 0 has infinitely many solutions

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