43. If A is defined by

$$A = \begin{bmatrix} B & 0 \\\ 0 & C \end{bmatrix}$$, show that A' is a c-inverse of A where

$$A' = \begin{bmatrix} B' & 0 \\\ 0 & C' \end{bmatrix}$$, where B' and C' are any c-inverses of B and C, respectively.