If a matrix A is skew-symmetric (Aᵀ = -A), what must be true about its diagonal entries?
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They are all zero
In a skew-symmetric matrix, the condition a_ij = -a_ji must hold. For diagonal elements where i=j, this implies a_ii = -a_ii, which can only be true if a_ii is zero.
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- What value must every diagonal entry of a skew-symmetric matrix take?