Prove statements (i), (ii), and (iii) of Lemma 17.1. Lemma 17.1. Let A be a U-centered distance

Prove statements (i), (ii), and (iii) of Lemma 17.1.

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Lemma 17.1. Let A be a U-centered distance matrix. Then 1. Rows and columns of A sum to zero. 2. (A) = . That is, if B is the matrix obtained by U-centering an element A. A Hn, B = A. 3. A is invariant to double centering. That is, if B is the matrix obtained by double centering the matrix A, then B = A. 4. If c is a constant and B denotes the matrix obtained by adding c to the off-diagonal elements of A, then B = A.