Let ∆ = 0 and ∆ c denotes the determinant of cofactors, then ∆ c = ∆ n – 1 , where n (>…

Let ∆ = 0 and ∆^c denotes the determinant of cofactors, then ∆^c = ∆^{n – 1}, where n (> 0) is the order of ∆.
On the basis of above information, answer the following questions :
If l₁, m₁, n₁ ; l₂, m₂, n₂ ; l₃, m₃, n₃ are real quantities satisfying the six relations :
\(\ell_{1}^{2}+\mathrm{m}_{1}^{2}+\mathrm{n}_{1}^{2}\)= \(\ell_{2}^{2}+\mathrm{m}_{2}^{2}+\mathrm{n}_{2}^{2}\)=\(\ell_{3}^{2}+\mathrm{m}_{3}^{2}+\mathrm{n}_{3}^{2}\)= 1
l₂ l₃ + m₂ m₃ + n₂ n₃ = l₃ l₁ + m₃ m₁ + n₃ n₁ =
l₁ l₂ + m₁ m₂ + n₁ n₂ = 0, then the value of
\[\left|\begin{array}{lll} \ell_{1} & \mathrm{~m}_{1} & \mathrm{n}_{1} \\ \ell_{2} & \mathrm{~m}_{2} & \mathrm{n}_{2} \\ \ell_{3} & \mathrm{~m}_{3} & \mathrm{n}_{3} \end{array}\right|\] is