5. Show that the g-inverse of a general 2 x 2 symmetric matrix A of rank 1 defined by

$$A = \begin{bmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{bmatrix}$$

is given by

$$A = \begin{bmatrix} a_{11} & a_{12} \\ T & T \\ a_{21} & a_{22} \\ T & T \end{bmatrix}$$

where T = a11 + a12 + a21 + a22 = tr (A'A).