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  4. If A is a matrix of order 3, such that A (adj A) = 10 I, then |adj A| =

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Q. If $A$ is a matrix of order $3$, such that $A (adj A) = 10\, I$, then $|adj A| $ =

KCETKCET 2014Determinants

Solution:

Given, $A(adj A)=10 I$
We know, $A(adj A)=|A| I$
$\therefore 10 I=|A| I$
$\Rightarrow |A| =10$
$\therefore \mid$ adj $\left. A|=| A\right|^{3-1}=(10)^{2}=100$