60. If A and B are defined as in Prob. 56, show that C is nonsingular, where

$$C = \begin{bmatrix} A & B \\ B' & 0 \end{bmatrix}$$

and show that

$$C^{-1} = \begin{bmatrix} A^{-1} & B' \\ B^{-1} & 0 \end{bmatrix}$$