NCERT Class 12 Maths · Chapter 4 Determinants · Miscellaneous Exercise Question 5

✅ Step-by-Step Solution

1. Expand the determinant along row 1, using cofactors Cᵢⱼ=(−1)ⁱ⁺ʲMᵢⱼ.
2. The cofactors in this row are \(\left[\begin{matrix}- x^{2} + x y + y^{2} & x^{2} + x y - y^{2} & - x^{2} - x y - y^{2}\end{matrix}\right]\).
3. The expansion terms are \(- x^{3} + x^{2} y + x y^{2}\), \(x^{2} y + x y^{2} - y^{3}\), \(- x^{3} - 2 x^{2} y - 2 x y^{2} - y^{3}\).
4. Adding and simplifying gives det A = \(- 2 \left(x + y\right) \left(x^{2} - x y + y^{2}\right)\).