Compact Schemes for $A^{+}B$, $A^{+}AB$ and $A{A}^{+}B$

Explicit details are presented for calculation of $A^{+}B$, $A^{+}AB$ and $A{A}^{+}B$ 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).