It is well known (and shown several times on this site) that if we have a matrix so that each row sums to zero then the matrix must be singular. I am curious if the following partial converse is known: if I have a matrix so that every row sums to 1 (or any other nonzero constant, but the same row sum for each row), must the matrix be nonsingular? I have some computational evidence for this but my guess is I am either missing an easy proof or a counterexample. Thanks!
2026-03-29 22:25:05.1774823105
Matrix with constant row sum
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Counterexample: consider $$ A = \pmatrix{1&1\\1&1} $$ In general, any matrix with repeated rows (or columns) is singular.