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If each element, of a determinant of third order with value $A$, is multiplied by 3 , then the value of newly formed determinant is
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Verified Answer
The correct answer is:
27A
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 .
$$
\therefore \quad|3 P|=3^3|P|=27 A
$$
Then, $|K P|=K^n|P|$, where $K$ is constant.
Given $|P|=A$, where $P$ is of order 3 .
$$
\therefore \quad|3 P|=3^3|P|=27 A
$$
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