Prove that vmatrix a^2+1 & ab & ac ab & b^2+1 & bc ac & bc & c^2+1 vmatrix =…

MATHEMATICS · Subjective · CBSE · Mathematics · Determinants · Determinants

Problem

Prove that ∣a2+1abacabb2+1bcacbcc2+1∣=1+a2+b2+c2.\begin{vmatrix} a^2+1 & ab & ac \\ ab & b^2+1 & bc \\ ac & bc & c^2+1 \end{vmatrix} = 1+a^2+b^2+c^2.

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