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Suppose that A and B are nxn matrices with A row equivalent to B. Prove that if A is nonsingular, then B is row equivalent to In.

I answered this on a test and it seemed right to me, but got zero credit. What did I do wrong? Was my logic incorrect?

my answer:

By definition, row equivalence means one matrix can be reduced to another. By definition, an invertible matrix can be row reduced to I, and is row equivalent to I. Since A is invertible, and thus row equivalent to I, B is row equivalent to I, since B is row equivalent to A.

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    $\begingroup$ Seems ok to me :/ $\endgroup$ – Hippalectryon Oct 7 '14 at 19:56
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    $\begingroup$ Your logic seems right to me. (It's probably a theorem in your book, rather than a definition, that an invertible matrix can be row-reduced to I, but that's a minor point.) $\endgroup$ – user84413 Oct 7 '14 at 22:15

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