Question

The value of determinant of lower triangular matrix $\left[\begin{array}{ccc}a& 0& 0\\ d& b& 0\\ e& f& c\end{array}\right]$ is

• A. $def$
• B. $abc$
• C. $0$
• D. None of these

Answer 1

The correct option is B $abc$

Given matrix
$\left[\begin{array}{ccc}a& 0& 0\\ d& b& 0\\ e& f& c\end{array}\right]$

$\therefore \left|\begin{array}{ccc}a& 0& 0\\ d& b& 0\\ e& f& c\end{array}\right|=a(bc-0)-0+0=abc$

Or,
From property, we can directly say that Determinant of upper or lower triangular square matrix is equal​ to product of its diagonal elements .