WBJEE · Maths · Determinants
If \(a, b, c\) are positive real numbers each distinct from unity, then the value of the determinant
\(\left|\begin{array}{ccc}1 & \log _a b & \log _a c \\ \log _b a & 1 & \log _b c \\ \log _c a & \log _c b & 1\end{array}\right|\) is
- A \(0\)
- B \(1\)
- C \(\log _{\mathrm{e}}(\mathrm{abc})\)
- D \(\log _e a \log _e b \log _e c\)
Answer & Solution
Correct Answer
(A) \(0\)
Step-by-step Solution
Detailed explanation
Expanding through first row, \(\log _{\mathrm{b}} a=\frac{1}{\log _{\mathrm{a}} \mathrm{b}}\) (by property)
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