Matrices -- Small Problem in Proof

I have a problem with your notation.
You clearly defined A ={a}ij
As long as you defined your notation then all is good.
However, you then went on to say that {c}ij = some summation which equals the ij element of C. But according to your definition, {c}ij equals C.

Be careful!
 
Also, I would not say that A is 0. I would say that A is the 0 matrix!
 
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