Can Matrix Addition Allow for Cancellation?

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The discussion centers on the mathematical property of matrix addition, specifically addressing the equation A + B = A + C. It concludes that if A, B, and C are matrices and this equation holds, then B must equal C, allowing for the cancellation of A from both sides. This cancellation is justified as a fundamental property of matrix addition, emphasizing the importance of understanding basic properties in mathematical proofs.

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Ques.)-If A,B,C are three matrices such that A+B = A+C, then prove that B=C.

Can i cancel out the A's in LHS and RHS ?
 
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Yes, but...

Normally, a question like this is an exercise in demonstrating how useful operations (e.g. cancellation) can be derived from definitions or through the application of more basic properties.

If cancellation is on the list of basic properties you're using for this purpose, then citing that is all you need to do -- but I suspect the problem is not meant to be so trivial.
 

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