I was wondering if anyone could help me with this:
Suppose A is a m x n matrix and there exist n x m matrices C and D such that CA = In and AD = Im. Prove that m = n and C = D.
I have never done any proofs in math before , and I don't know where to even start with this. Like, what I did for myself was to give m and n concrete numbers, like make m = 2 and n = 2, and than when I did the "calculations" with a bit more concrete numbers, I see that m = n and C = D, but I am not sure how to "prove this" other than drawing pictures of matrices, and than seeing that C really is = D and Im = In.
Thank you for taking a look at this