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3 and 4 . determinant and metrices — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths3 and 4 . determinant and metrices1 Mark
MCQ
If $A = \left[ {\begin{array}{*{20}{c}}
a&0&0\\
0&a&0\\
0&0&a
\end{array}} \right]$ ; then $|A| |adjA|$ is equal to
  • A
    $a^{25}$
  • B
    $a^{27}$
  • C
    $a^{81}$
  • ✓
    $a^9$
✓

Answer

Correct option: D.
$a^9$
d
$\left| A \right|\left| {adj\,A} \right| = \left| {A \cdot adj\,A} \right| = \left| A \right|\left| I \right| = {\left| A \right|^3}\left| I \right| = {\left( {{a^3}} \right)^3} \cdot 1$

$\Rightarrow|\mathrm{A}||\operatorname{adj} \mathrm{A}|=\mathrm{a}^{9}$

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