How could I approach questions like the following?
If the first and third column of the matrix B are the same, will this be the case for the matrix AB as well ?
I'm not necessarily looking for a ready answer to this question. I just want to get an idea of how I should approach questions like this. Taking two random matrices and multiplying them wouldn't help alot, I think, because they can't prove anything. I would be only able to claim that for this case only the answer to the question is yes, but I'm looking for a way to get a certain answer for all cases. If I am to prove it wrong, a simple example of a case, where the answer is no, is enough. If such a case exists how am I to find hints about which exactly is this case?
Thank-you in advance.
PS. I'm not a native english speaker and everything I have done on linear algebra I have done it in my own language (Greek), so please forgive me if I use the wrong terminology. Just inform me of any mistakes I have done and I will repair them at once. If I haven't given enough or clear enough information, please don't hesitate to ask for clarifications.