Question: 46. In Prob. 45 let B = C 1 and partition B as $$B = begin{bmatrix} B_{11} & b_{12} b_{21} & b end{bmatrix}$$ where

46. In Prob. 45 let B = C−1 and partition B as

$$B = \begin{bmatrix} B_{11} & b_{12} \\ b_{21} & b \end{bmatrix}$$

where B₁₁ is an n x n submatrix. Show that

(1) b = 0,

(2) b12 = (1/n)1,

(3) 1'B11 = 0,

(4) AB11 and B11A are idempotent.

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