Can Matrix Addition Allow for Cancellation?

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In the discussion about matrix addition and cancellation, the main question is whether A+B = A+C implies B=C. It is confirmed that cancellation of A from both sides is valid under certain conditions. The conversation emphasizes that this exercise illustrates the usefulness of basic properties in matrix operations. However, there is a suggestion that the problem may not be intended to be straightforward, hinting at deeper implications in matrix theory. Understanding the foundational properties of matrix addition is crucial for addressing such questions effectively.
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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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