Mathematics - Matrices Question with Solution | TestHub

MathematicsMatricesAdjointMedium2 minPYQ_2022

MathematicsMediumsingle choice

Let $A$ be a $3 \times 3$ invertible matrix. If $|adj (24 A)| =$ $adj (3 adj (2 A)) |$ , then ${|A|}^{2}$ is equal to

Answer:

Solution:

We know that $|adj A| = {|A|}^{n - 1}$

$|K A| = K^{n} |A|$

where $n$ is order of matrix

Given

$|adj (24 A)| = |adj 3 (adj 2 A)|$

$\Rightarrow {|24 A|}^{2} = {|3 adj (2 A)|}^{2}$

$\Rightarrow |24 A| = |3 adj (2 A)|$

$\Rightarrow 24^{3} |A| = 3^{3} |adj 2 A|$ $\Rightarrow 24^{3} |A| = 3^{3} |2 A| |2 A|$

$\Rightarrow 24^{3} |A| = 3^{3} 2^{3} 2^{3} |A| |A|$

$\Rightarrow |A| = \frac{24^{3}}{2^{3} 2^{3} 3^{3}}$ $= \frac{{(2^{3} \cdot 3)}^{3}}{2^{6} 3^{3}}$ $= 8$

$\Rightarrow {|A|}^{2} = 64$

Stream:JEESubject:MathematicsTopic:MatricesSubtopic:Adjoint

⏱ 2mℹ️ Source: PYQ_2022

Loading discussions...