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Math Help - a question of matrix equations

  1. #1
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    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.
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  2. #2
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    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.

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  3. #3
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    Quote Originally Posted by rulin View Post
    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.
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