Let $J$ be a $n \times n$ matrix of 1's and $A$ is a $n \times m$ matrix with generalized inverse $G$. i.e. $AGA = A$.
I'm trying to find a generalized inverse of $GA$ and $J$.
Am I correct to say a generalized inverse of $GA$ is just itself, $GA$, since:
$GAGAGA = GAGA = GA$
and the generalized inverse of J is $\frac{1}{n}I_{n}$ since:
$J\frac{1}{n}I_{n}J =\frac{1}{n}J^{2} = \frac{n}{n}J = J$