43. If A is defined by $$ A = begin{bmatrix} B & 0 0 & C end{bmatrix} , $$ show that A is a

43. If A is defined by

$$

A =

\begin{bmatrix}

B & 0 \\

0 & C

\end{bmatrix}

,

$$

show that Aº is a c-inverse of A where

$$

Aº =

\begin{bmatrix}

Bº & 0 \\

0 & Cº

\end{bmatrix}

,

$$

where Bº and Cº are any c-inverses of B and C, respectively.