# Math Help - a question of matrix equations

1. ## a question of matrix equations

Prove:

1. Matrix equation $AXA=A$ has a solution always for every matrix $A$.

2. If both matrix equations $AY=C$ and $ZB=C$ have solution, then equation $AXB=C$ has a solution.

2. 1. Matrix equation $AXA=A$ has a solution always for every matrix $A$.
I think this would only work if A is nonsingular and X is the inverse.

3. Originally Posted by rulin
Prove:
2. If both matrix equations $AY=C$ and $ZB=C$ have solution, then equation $AXB=C$ has a solution.
I don't get it. The multiplication is defined by what you wrote.