I have been asked to show that if $A$ is an $n \times n$ reduced row echelon matrix, then either $A = I_n$ or $A$ has a zero row.

Intuitively I see why this is true, but I'm unsure how to show it mathematically?

  • 1
    $\begingroup$ There are n rows and each 1s must be further to the right than the ones above $\endgroup$ – Jean-Sébastien Feb 18 '16 at 21:20
  • $\begingroup$ @Jean-Sébastien So can I say that if it is not the identity, then there must exist a zero column, and because each leading entry is strictly to the right of the one above, we would clearly reach the last column before the last row and so the bottom one must be a zero row? $\endgroup$ – the man Feb 18 '16 at 21:24
  • $\begingroup$ Yup, depending on what's expected you might need to put that into maths but you've got the idea $\endgroup$ – Jean-Sébastien Feb 18 '16 at 21:28

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