If - 1 2 3 2 3 1 3 1 2 - then -adj adj A- is equal to

The correct option is C 18^4 |A| = #160; 1 amp; 2 amp; 3 2 amp; 3 amp; 1 3 amp; 1 amp; 2 #160; #160; ...

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Byju's Answer

Standard XII

Mathematics

Evaluation of a Determinant

If [ 1 2 ...

Question

If $⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 2 & 3 & 1 3 & 1 & 2 \end{matrix} ⎤ ⎥ ⎦$ then $| a d j (a d j A) |$ is equal to

18^{3}

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18^{2}

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18^{4}

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18^{6}

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Solution

The correct option is C $18^{4}$
$| A |$ $=$ $∣ ∣ ∣ ∣ \begin{matrix} 1 & 2 & 3 2 & 3 & 1 3 & 1 & 2 \end{matrix} ∣ ∣ ∣ ∣$
$=$ $1 (6 - 1) - 2 (4 - 3) + 3 (2 - 9)$ $=$ $- 18$

$| a d j (a d j (A)) |$ $=$ $| A |^{(n - 1)^{2}}$ **Properties of the determinants

$| a d j (a d j (A)) |$ $=$ $(- 18)^{(3 - 1)^{2}}$ $=$ $18^{4}$ $n = 3$ for the $m a t r i x$ of order $3$

So the correct option is $C$

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If ⎡⎢⎣123231312⎤⎥⎦ then |adj (adj A)| is equal to

The correct option is C 184|A| = ∣∣ ∣∣123231312∣∣ ∣∣ = 1(6−1)−2(4−3)+3(2−9) = −18|adj(adj(A))| = |A|(n−1)2 **Properties of the determinants|adj(adj(A))| = (−18)(3−1)2 = 184 n=3 for the matrix of order 3So the correct option is C

If $⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 3 2 & 3 & 1 3 & 1 & 2 \end{matrix} ⎤ ⎥ ⎦$ then $| a d j (a d j A) |$ is equal to