Can Matrix Addition Allow for Cancellation?

[johncena]

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 ?

 

[Hurkyl]

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.