Let 𝑀 = (𝐼n βˆ’ (1/n) πŸπŸα΅€) be a matrix, where 𝟏 = (1,1,1,…,1)α΅€ ∈ ℝn and 𝐼n…

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Let 𝑀 = (𝐼n βˆ’ (1/n) πŸπŸα΅€) be a matrix, where 𝟏 = (1,1,1,…,1)α΅€ ∈ ℝn and 𝐼n is the identity matrix of order n. Which of the following options is/are correct?

  1. A.

    𝑀ᡀ = 𝑀

  2. B.

    𝑀2 = 𝐼n

  3. C.

    Trace(𝑀) = n

  4. D.

    𝑀 is a projection matrix

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