First slide

Applications of determinant

Question

$If A is 3 order square matrix such that | A | = 2 then$ $|ad j (a d j (a d j A))| is$

Moderate

A

512
B

256
C

64
D

None of these

Solution

We know that
${ladj (adj A) | = | A|}^{(n - 1)^{2}}$
${\Rightarrow ladj (adj (adj A)) |= lad j A^{(n - 1)^{2}} =| A|}^{(n - 1)^{3}}$
$= 2^{8} = 256$

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