Its not a homework, lol. Just an interesting problem, that i don't quite understand. I think that the only option is that A matrix is zero matrix or maybe i have forgotten some theorem or criteria

Let for j = 0,. . ., n aj = a0 + jd, where a0 and d are fixed real numbers.
Calculate the determinant of the matrix A of size (n + 1) × (n + 1). Matrix A is below

Let a 3 × 3 matrix A be such that for any vector of a column v ∈ R3 the vectors Av and v are orthogonal. Prove that At + A = 0, where At is the transposed matrix.

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