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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 $A = \left[ {\begin{array}{*{20}{c}}3&1\\{ - 1}&2\end{array}} \right]$, then ${A^2} = $
  • A
    $\left[ {\begin{array}{*{20}{c}}8&{ - 5}\\{ - 5}&3\end{array}} \right]$
  • B
    $\left[ {\begin{array}{*{20}{c}}8&{ - 5}\\5&3\end{array}} \right]$
  • C
    $\left[ {\begin{array}{*{20}{c}}8&{ - 5}\\{ - 5}&{ - 3}\end{array}} \right]$
  • ✓
    $\left[ {\begin{array}{*{20}{c}}8&5\\{ - 5}&3\end{array}} \right]$
✓

Answer

Correct option: D.
$\left[ {\begin{array}{*{20}{c}}8&5\\{ - 5}&3\end{array}} \right]$
d
(d) $A = \left[ {\begin{array}{*{20}{c}}3&1\\{ - 1}&2\end{array}} \right]$

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

${A^2} = \left[ {\begin{array}{*{20}{c}}8&5\\{ - 5}&3\end{array}} \right]$.

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