The value of \( \begin{vmatrix}1 & \log_b a\\\log_a b & 1\end{vmatrix} \) is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 0
\( \displaystyle \begin{vmatrix}1 & \log_b a\\\log_a b & 1\end{vmatrix}=1-\log_b a\cdot\log_a b \)
By the change of base rule, \( \log_b a=\frac{\log a}{\log b} \) and \( \log_a b=\frac{\log b}{\log a} \), so their product is 1:
\( \displaystyle 1-1=0 \)