Question

If $\left[\begin{array}{cc}1& {\log }_{b}a\\ {\log }_{a}b& 1\end{array}\right]$ then $|A|$ is equal to

• A. $0$
• B. ${\log }_{a}b$
• C. $-1$
• D. ${\log }_{b}a$

Answer 1

Answer: (A)

Given, $A=\left[\begin{array}{cc}1& {\log }_{b}a\\ {\log }_{a}b& 1\end{array}\right]$
$\Rightarrow |A|=\left[\begin{array}{cc}1& \frac{\log a}{\log b}\\ \frac{\log b}{\log a}& 1\end{array}\right]=1-1=0$