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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 $A = \left[ {\begin{array}{*{20}{c}}1&3\\2&1\end{array}} \right]$, then determinant of ${A^2} - 2A$ is
  • A
    $5$
  • ✓
    $25$
  • C
    $-5$
  • D
    $-25$
✓

Answer

Correct option: B.
$25$
b
(b) $A = \left| {\,\begin{array}{*{20}{c}}
1&3\\
2&1
\end{array}\,} \right| $

 ${A^2} = \left[ {\begin{array}{*{20}{c}}1&3\\2&1\end{array}} \right]\,\left[ {\begin{array}{*{20}{c}}1&3\\2&1\end{array}} \right]\, = \,\left[ {\begin{array}{*{20}{c}}7&6\\4&7\end{array}} \right]$

and ${A^2} - 2A = \left[ {\begin{array}{*{20}{c}}5&0\\0&5\end{array}} \right]\,,{\rm{det }}({A^2} - 2A) = \left| {\,\begin{array}{*{20}{c}}5&0\\0&5\end{array}\,} \right| = 25$.

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