If each element, of a determinant of third order with value $A$, is multiplied by 3 , then the value of…
If each element, of a determinant of third order with value $A$, is multiplied by 3 , then the value of newly formed determinant is
3A
9A
27A
-27A
Solution
Since, we know that, if $P$ is any matrix of order n.
Then, $|K P|=K^n|P|$, where $K$ is constant.
Given $|P|=A$, where $P$ is of order 3 .
$
\therefore \quad|3 P|=3^3|P|=27 A
$