# What is sum of rows of Hadamard matrix

Suppose A is a Hadamard matrix of size $d$. Let A be in normalized in a sense that first row and first column are all ones. What is the sum of rows? I tried random Hadamard matrices and seem to get $d,0,0,0,0,\ldots$

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Follows immediately from the property of Hadamard Matrices: Any two distinct rows are orthogonal.

Since all the other rows are orthogonal to the all ones row, the sum of the elements in each of those rows must be zero.