a question of matrix equations

Apr 2010
3
1
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.
 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
1. Matrix equation \(\displaystyle AXA=A\) has a solution always for every matrix \(\displaystyle A\).
I think this would only work if A is nonsingular and X is the inverse.

 

dwsmith

MHF Hall of Honor
Mar 2010
3,093
582
Florida
Prove:
2. If both matrix equations \(\displaystyle AY=C\) and \(\displaystyle ZB=C\) have solution, then equation \(\displaystyle AXB=C\) has a solution.
I don't get it. The multiplication is defined by what you wrote.