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 zeroSolution : Let A be a 4 × 4 real symmetric orthogonal matrix. $$=> A^T= A$$ and $$AA^T=A^TA=I$$ from these two equations $$=>A^2=I$$ $$=> (A-I)(A+I)=0$$ \[.=>A=I…

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