Compact Schemes for $A^+B$, $A^+AB$ and $AA^+B$

Explicit details are presented for calculation of $A^+B$, $A^+AB$ and $AA^+B$ where $A_{m\times n}$ is any nonzero matrix, $A^+$ is the Moore-Penrose pseudoinverse of $A$ and $B$ is any matrix of appropriate dimensions, where the quantities in question are found using only the storage originally allocated to the matrices $A$ and $B$ (together with some simple one dimensional indexing arrays).