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Echelon form of matrix have the same rank, after operations modulo

Discussion in 'Mathematics' started by Jonny, Oct 8, 2018.

  1. Jonny

    Jonny Guest

    In my homework task, I need to prove that if my matrix have rank $k$ modulo $\ell$, then it also have rank $k$ modulo $p$. Please give me advice, how to prove it.

    --edit--

    The precise task is:

    On the diagonal of square matrix of order $n$ are $0$s, other places are $1$ or $2012$. Prove that the rank of this matrix is $n$ or $n-1$. Consider modulo function.

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