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Memory Based GATE DA 2024 | Question: 5

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Consider a matrix \(M \in \mathbb{R}^{3 \times 3}\) and let \(U\) be a 2-dimensional subspace such that \(M\) is a projection onto \(U\). Which of the following statements are true?
  1. \(M^3 = M\)
  2. \(M^2 = M\)
  3. The nullspace of \(M\) is 1-dimensional.
  4. The nullspace of \(M\) is 2-dimensional.
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