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  4. If [1& logb a loga b&1] then |A| is equal to

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Q. If $\begin{bmatrix}1&\log_{b} a\\ \log_{a} b&1\end{bmatrix}$ then $|A|$ is equal to

COMEDKCOMEDK 2012Determinants

Solution:

Given, $A = \begin{bmatrix}1&\log_{b} a\\ \log_{a} b&1\end{bmatrix}$
$\Rightarrow \ |A| = \begin{bmatrix}1&\frac{\log a }{\log b}\\ \frac{\log b}{\log a}&1\end{bmatrix} = 1 - 1=0$