Question:medium
If the product \( abc = 1 \), then the value of the determinant \( \begin{vmatrix} -a^2 & ab & ac \\ ba & -b^2 & bc \\ ac & bc & -c^2 \end{vmatrix} \) is
If the product \( abc = 1 \), then the value of the determinant \( \begin{vmatrix} -a^2 & ab & ac \\ ba & -b^2 & bc \\ ac & bc & -c^2 \end{vmatrix} \) is
Show Hint
Look for symmetry in determinants to simplify quickly.
Updated On: Apr 30, 2026
- \(1\)
- \(2\)
- \(3\)
- \(4\)
- \(5\)
Show Solution
The Correct Option is C
Solution and Explanation
Was this answer helpful?
0
Top Questions on Properties of Determinants
- If \(\alpha \neq a\), \(\beta \neq b\), \(\gamma \neq c\) and \[ \begin{vmatrix} \alpha & b & c \\ a & \beta & c \\ a & b & \gamma \end{vmatrix} = 0,\] then \[ \frac{a}{\alpha - a} + \frac{b}{\beta - b} + \frac{\gamma}{\gamma - c} \] is equal to:
- JEE Main - 2024
- Mathematics
- Properties of Determinants
- The value of vmatrix 1 & 2 & 3
-4 & 3 & 6
2 & -7 & 9 vmatrix is- BITSAT - 2010
- Mathematics
- Properties of Determinants
- If A=bmatrix2&0&0
2&2&0
2&2&2bmatrix, then det(adj A) is equal to:- BITSAT - 2011
- Mathematics
- Properties of Determinants
- If beginvmatrix p & q-y & r-z
p-x & q & r-z
p-x & q-y & r endvmatrix=0, then the value of (p)/(x)+(q)/(y)+(r)/(z) is- BITSAT - 2021
- Mathematics
- Properties of Determinants
- Want to practice more? Try solving extra ecology questions todayView All Questions
