Show that there does not exist any 4 × 4 real symmetric orthogonal matrix with all diagonal elements zero

Question : Show that there does not exist any 4 × 4 real symmetric orthogonal matrix with all diagonal elements zero Solution : Let A be a 4 × 4 real symmetric orthogonal matrix. \[=> A^T= A\] and \[ AA^T=A^TA=I\]…

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