WBJEE · Maths · Determinants
The value of determinant \(\left|\begin{array}{ccc}1+a^{2}-b^{2} & 2 a b & -2 b \\ 2 a b & 1-a^{2}+b^{2} & 2 a \\ 2 b & -2 a & 1-a^{2}-b^{2}\end{array}\right|\) is
- A 0
- B \(\left(1+a^{2}+b^{2}\right)\)
- C \(\left(1+a^{2}+b^{2}\right)^{2}\)
- D \(\left(1+a^{2}+b^{2}\right)^{3}\)
Answer & Solution
Correct Answer
(D) \(\left(1+a^{2}+b^{2}\right)^{3}\)
Step-by-step Solution
Detailed explanation
Let \(\Delta=\left|\begin{array}{ccc}1+a^{2}-b^{2} & 2 a b & -2 b \\ 2 a b & 1-a^{2}+b^{2} & 2 a \\ 2 b & -2 a & 1-a^{2}-b^{2}\end{array}\right|\) Apply \(\mathrm{C}_{\mathrm{1}} \rightarrow \mathrm{C}_{1}-\mathrm{bC}_{3}\) and…
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