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Good Evening All

I am trying to prove that if you have two m x n matrices A and B both in rref form, then the kernel of the homomorphism defined by A equals the kernel of the homomorphism defined by B iff A = B

Obviously the reverse implication is true.

I am stuck one the 1st implication.

I was thinking of doing a proof by induction, starting with an m x 1 matrix and then showing that if it is true for an m x n matrix, it must be true for an m x n+1 matrix, but I am not sure of that is the smart way of going about it.

Thanks

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    I know that is definitely true, but I am not sure why that helps/is needed as the matrices A and B are already in rref form – 2017-02-26
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    I am still confused, unfortunately. I am not creating equivalent matrices. I am stating that I have two matrices A and B, which are already in rref and have the same nullspace. Prove that A and B must be equal. Note: I also am using this as a lemma to prove that the rref form of a matrix is unique so I cannot assume currently that rref(A) is unique – 2017-02-26
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    haha sounds good thanks for the help – 2017-02-26

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