The sum of the elements in each row of \(A\in\mathbb{R}^{n\times n}\) is 1. If…

GATE · 2025 · DA · Data Science & AI

The sum of the elements in each row of A∈Rn×nA\in\mathbb{R}^{n\times n} is 1. If B=A3−2A2+AB=A^3-2A^2+A, which one of the following statements is correct (for x∈Rnx\in\mathbb{R}^n)?

  1. A.

    The equation Bx = 0 has no solution

  2. B.

    The equation Bx = 0 has exactly two solutions

  3. C.

    The equation Bx = 0 has infinitely many solutions

  4. D.

    The equation Bx = 0 has a unique solution

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