Prove:
1. Matrix equation $\displaystyle AXA=A$ has a solution always for every matrix $\displaystyle A$.
2. If both matrix equations $\displaystyle AY=C$ and $\displaystyle ZB=C$ have solution, then equation $\displaystyle AXB=C$ has a solution.
Prove:
1. Matrix equation $\displaystyle AXA=A$ has a solution always for every matrix $\displaystyle A$.
2. If both matrix equations $\displaystyle AY=C$ and $\displaystyle ZB=C$ have solution, then equation $\displaystyle AXB=C$ has a solution.