How can I show that $(A^T)^+=(A^+)^T$, where $A^+$ is Moore-Penrose Inverse?
I know there are 4 properties of the Moore-Penrose Generalized inverse, for example: $$AA^+A=A^+. $$
To prove it, could I take the transpose of the above $$(AA^+A)^T=(A^+)^T$$ and somehow simplify the LHS so it looks like the LHS of the original statement? Is this on the right track at all? I can get the LHS to be: $$A^+A(A^+)^T$$ but this does not seem to help me.
Any hints please?