If A -begin bmatrix 1 2 -1-1 1 2112 -1 1lend bmatrix- then detAdjAdj A isA- 144B- 146C- 149D- 142

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Standard X

Mathematics

Addition and Subtraction of a Matrix

If A =begin b...

Question

If A = $⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & - 1 - 1 & 1 & 2 2 & - 1 & 1 \end{matrix} ⎤ ⎥ ⎦$ , then det (Adj (Adj A)) is

(14)^{4}

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(14)^{6}

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(14)^{9}

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(14)^{2}

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Solution

The correct option is A $(14)^{4}$
$| A | = (1 + 2) - 2 (- 1 - 4) - 1 (1 - 2)$
$= 3 + 10 + 1 = 14$
$∴ d e t (A d j (A d j A)) = | A d j A |^{2} = | A |^{4} = (14)^{4}$

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If A = ⎡⎢⎣12−1−1122−11⎤⎥⎦, then det (Adj (Adj A)) is

The correct option is A (14)4|A|=(1+2)−2(−1−4)−1(1−2) =3+10+1=14 ∴det (Adj (Adj A))=|Adj A|2=|A|4=(14)4

If A = $⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & - 1 - 1 & 1 & 2 2 & - 1 & 1 \end{matrix} ⎤ ⎥ ⎦$ , then det (Adj (Adj A)) is

The correct option is A $(14)^{4}$
$| A | = (1 + 2) - 2 (- 1 - 4) - 1 (1 - 2)$
$= 3 + 10 + 1 = 14$
$∴ d e t (A d j (A d j A)) = | A d j A |^{2} = | A |^{4} = (14)^{4}$