[math] \newcommand{\mathds}{\mathbb}[/math]

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Find the defect of the following matrix,

[[math]] K_4=\begin{pmatrix} -1&1&1&1\\ 1&-1&1&1\\ 1&1&-1&1\\ 1&1&1&-1 \end{pmatrix} [[/math]]

via the simplest possible proof.