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Matrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsMatrices1 Mark
MCQ
If $A$ is square matrix of order 3 , then $\left|\operatorname{Adj}\left(\operatorname{Adj} A^2\right)\right|=$
  • A
    $|A|^2$
  • B
    $|A|^4$
  • ✓
    $|A|^8$
  • D
    $|A|^{16}$
✓

Answer

Correct option: C.
$|A|^8$
c. $|A|^8$

$∣​\text{adj}(\text{adj}\text{A}^2)​∣​=\text{Q}=\begin{vmatrix}\text{A}^2\end{vmatrix}^{(3-1)^2} =\begin{vmatrix}\text{ A}^2 \end{vmatrix} ^4 =\begin{vmatrix} \text{A}\end{vmatrix}^8$

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