Determinant Identities and Properties (Jee Mains)

Determinants

Hard

Determinant Identities and Properties

Among the statements :
I : If $\left| {\begin{array}{*{20}{c}} 1&{\cos \alpha }&{\cos \beta }\\[0.9em] {\cos \alpha }&1&{\cos \gamma }\\[0.9em] {\cos \beta }&{\cos \gamma }&1 \end{array}} \right|$ = $\left| {\begin{array}{*{20}{c}} 0&{\cos \alpha }&{\cos \beta }\\[0.9em] {\cos \alpha }&0&{\cos \gamma }\\[0.9em] {\cos \beta }&{\cos \gamma }&0 \end{array}} \right|$ , then cos²α + cos²β + cos²γ =, and
II : If $\left| {\begin{array}{*{20}{c}} {{x^2} + x}&{x + 1}&{x - 2}\\[0.9em] {2{x^2} + 3x - 1}&{3x}&{3x - 3}\\[0.9em] {{x^2} + 2x + 3}&{2x - 1}&{2x - 1} \end{array}} \right|$ = px + q, then p² = 196q²,

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