Let \(A\in\mathbb{R}^{n\times n}\) be such that A3=A. Which one of the…

GATE · 2025 · DA · Data Science & AI

Let A∈Rn×nA\in\mathbb{R}^{n\times n} be such that A3=A. Which one of the following statements is ALWAYS correct?

  1. A.

    A is invertible

  2. B.

    Determinant of A is 0

  3. C.

    The sum of the diagonal elements of A is 1

  4. D.

    A and A2 have the same rank

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