Where to begin when comparing matrices and their inverses

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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?




matrices inverse




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    up vote
    0
    down vote

    favorite












    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?




    matrices inverse




    share|cite|improve this question





















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      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?




      matrices inverse




      share|cite|improve this question











      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?





      matrices inverse





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked 2 days ago









      Phatfoo

      42




      42




















          1 Answer
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          up vote
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          down vote













          Looking at e.g. the $2times 2$ 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?






          share|cite|improve this answer





















          • I'm not sure I'm understanding your comment. Why would I want the matrices to be real numbers?
            – Phatfoo
            2 days ago










          • 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?!
            – Jonas Lenz
            2 days ago










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          1 Answer
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          1 Answer
          1






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes








          up vote
          0
          down vote













          Looking at e.g. the $2times 2$ 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?






          share|cite|improve this answer





















          • I'm not sure I'm understanding your comment. Why would I want the matrices to be real numbers?
            – Phatfoo
            2 days ago










          • 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?!
            – Jonas Lenz
            2 days ago














          up vote
          0
          down vote













          Looking at e.g. the $2times 2$ 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?






          share|cite|improve this answer





















          • I'm not sure I'm understanding your comment. Why would I want the matrices to be real numbers?
            – Phatfoo
            2 days ago










          • 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?!
            – Jonas Lenz
            2 days ago












          up vote
          0
          down vote










          up vote
          0
          down vote









          Looking at e.g. the $2times 2$ 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?






          share|cite|improve this answer













          Looking at e.g. the $2times 2$ 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?







          share|cite|improve this answer













          share|cite|improve this answer



          share|cite|improve this answer











          answered 2 days ago









          Jonas Lenz

          326211




          326211











          • I'm not sure I'm understanding your comment. Why would I want the matrices to be real numbers?
            – Phatfoo
            2 days ago










          • 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?!
            – Jonas Lenz
            2 days ago
















          • I'm not sure I'm understanding your comment. Why would I want the matrices to be real numbers?
            – Phatfoo
            2 days ago










          • 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?!
            – Jonas Lenz
            2 days ago















          I'm not sure I'm understanding your comment. Why would I want the matrices to be real numbers?
          – Phatfoo
          2 days ago




          I'm not sure I'm understanding your comment. Why would I want the matrices to be real numbers?
          – Phatfoo
          2 days ago












          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?!
          – Jonas Lenz
          2 days ago




          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?!
          – Jonas Lenz
          2 days ago












           

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