0
$\begingroup$

I've just started with linear algebra and am NOT looking for the answer. I'm just looking for a way to begin answering the following true/false question:

If A,B,C are matrices of the same size such that A+C=B+C then A=B and A(−1) =B(−1)

The A(-1) and B(-1) are the inverses of A and B.

Should I create, let's say, a 2x2 matrix (with any numbers) for A, B, and C?

If so, then what would be my next step?

$\endgroup$
0
$\begingroup$

Looking at e.g. the $2\times 2$ case may give an intuition whether a statement is wrong or false and might even give an idea how to prove/disprove the statement rigorously. Nevertheless, this does not give a proof.

How would you proceed in case that $A,B,C$ would not be matrices but, let us say real numbers?

And moreover, why can we even say what the inverse of the matrix $A$ is?

$\endgroup$
2
  • $\begingroup$ I'm not sure I'm understanding your comment. Why would I want the matrices to be real numbers? $\endgroup$ – Phatfoo Aug 4 '18 at 14:15
  • $\begingroup$ Real numbers are just one-dimensional matrices. Also the set of matrices of fixed size as well as the real numbers form a group with respect to addition. The first part of the statement can be generalized to arbitrary groups. I was proposing to look at the real numbers because the reals are a maybe easier to understand or to have intuition whether a statement holds. Moreover, I assume that you are working with matrices over some field?! $\endgroup$ – Jonas Lenz Aug 4 '18 at 14:22

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.