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Proof : Sum of Matrix Columns

If the sum of any of the columns of a matrix is 1 and that of any row is 1 then prove that there are equal number of rows and columns.

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As stated in the problem,

(sum of all the elements of the matrix) = (Number of columns) * (sum of ...

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A proof for sums of matrix columns is provided. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.